Geometry

A triangle is shown in the diagram. Based on the lengths of its sides, what is the most specific name for this triangle?

Which property is shared by both a rectangle and a square?

What is the name of a triangle where all three sides have different lengths?

Which of these quadrilaterals must have all four sides of equal length, but does not necessarily have right angles?

If the sum of three angles in a quadrilateral is $275^{\circ}$, what is the size of the fourth angle?

A quadrilateral has one pair of parallel sides of lengths 5 cm and 8 cm. The other two sides are both 4 cm. What is the most specific name for this shape?

What is the size of each interior angle in a regular triangle?

A kite-shaped window has one diagonal that is $120$ cm long and another that is $80$ cm long. If the shorter diagonal is bisected by the longer one at a right angle, and the top two sides are $50$ cm each, what is the length of the bottom two sides? (Note: Classification is Kite).

A garden plot is in the shape of a quadrilateral with vertices $P(2, 2)$, $Q(6, 2)$, $R(6, 5)$, and $S(2, 5)$ on a coordinate grid. What is the most specific classification for this garden plot?

A folding table has a support frame that forms a triangle with angles $40^{\circ}$ and $100^{\circ}$. What must be the value of the third angle, and how is the triangle classified by its angles?

If two angles are on a straight line and one measures $75^{\circ}$, what is the measure of the other angle?

What angle is formed by the hands of a clock when it is exactly 3:00?

Which instrument is most commonly used to measure the size of an angle in degrees?

A square has four interior angles. What is the sum of these angles?

In the diagram, four angles meet at a point. Three are $85^{\circ}$, $95^{\circ}$, and $100^{\circ}$. What is the fourth angle?

Calculate the value of angle $y$ in the diagram where a line bisects a $120^{\circ}$ angle into two equal parts.

A right-angled isosceles triangle has one angle of $90^{\circ}$. What are the other two angles?

In a geometry sketch, a student draws a square and then draws a diagonal. What is the measure of the angle between the diagonal and any one of the sides of the square?

A fan is opened such that the outermost blades form a straight line ($180^{\circ}$). If there are 5 equal angles between the 6 blades of the fan, what is the measure of each angle between two adjacent blades?

A student uses a compass to draw a circle and then marks two points $P$ and $Q$ on the circumference. If the angle $POQ$ (where $O$ is the center) is a right angle and he draws a third point $R$ such that $\angle QOR$ is $35^{\circ}$ and $R$ is outside the angle $POQ$, what is the total measure of $\angle POR$?

On a straight line, one angle is $135^\circ$. What is the other angle $k$?

Which of these is the correct sum for angles at a point?

A straight line is divided into three angles: $50^\circ$, $x$, and $40^\circ$. Calculate $x$.

Find the value of the missing angle $p$ in this right-angled configuration on a line.

Two intersecting lines form an angle of $150^\circ$. What is the size of the smaller adjacent angle?

Three angles on a line are $x$, $x+20^\circ$, and $x-20^\circ$. Find $x$.

Five angles of equal size meet at a point. What is the size of each angle?

At a traffic junction, five roads meet. The angles between the roads are $a$, $b$, $c$, $d$, and $e$. Road 1 and Road 3 form a straight line ($a + b = 180^\circ$). If $c = 40^\circ$ and $d = 2c$, find the value of angle $e$ if it is known that $e$ and $c+d$ are supplementary.

On a straight line $ABC$, a ray $BD$ is drawn. If angle $ABD = (x^2 + 20)^\circ$ and angle $DBC = (8x + 60)^\circ$, and $x$ is a positive integer, determine the value of $x$.

A logic puzzle shows three lines intersecting at a single point $M$. The angles are labeled in order as $x$, $y$, $x$, $y$, $x$, $y$ around the point. If $x = 2y - 30$, find the value of $y$.

One angle in a triangle is $120^{\circ}$ and another is $15^{\circ}$. Find the third angle.

What is the sum of the interior angles of any triangle?

In a triangle, the angles are $x$, $2x$, and $90^{\circ}$. Find the value of $x$.

Find the value of $x$ in this right-angled triangle.

In a right-angled isosceles triangle, what is the size of each of the two smaller angles?

The diagram shows a triangle with an exterior angle. Calculate the value of $w$.

One angle of a triangle is $x$, the second is $x + 20$, and the third is $x + 40$. Find the value of $x$.

A triangular sail has angles such that the second angle is $30^{\circ}$ more than the first, and the third angle is $30^{\circ}$ more than the second. What type of triangle is it?

A carpenter cuts a piece of wood into a triangle. The first angle is $50^{\circ}$. The second angle is $15^{\circ}$ smaller than the third angle. Find the size of the third angle.

In triangle $PQR$, angle $P$ is twice the size of angle $Q$, and angle $R$ is three times the size of angle $Q$. What is the measure of the smallest angle?

The diagram shows a rectangle labeled $R$. If rectangle $R$ is reflected in the horizontal dashed line (the mirror line), what will be the coordinates of the new bottom-left corner?

A scalene triangle has how many lines of symmetry?

In the diagram, the shape is reflected in the line $L$. What is the distance of the image from line $L$ if the original is $4$ units away?

A shape is rotated $90^{\circ}$ clockwise. If it was pointing North (Up), which direction is it pointing now?

In the diagram, shape $T$ is rotated $180^{\circ}$ about the origin. If one vertex of $T$ is at $(-2, -4)$, where is the corresponding vertex of the image?

A shape is formed by two overlapping congruent circles as shown. How many lines of symmetry does the combined shape have?

If a rectangle has vertices at $(1, 1), (4, 1), (4, 3),$ and $(1, 3)$, and it is reflected across the line $x = 5$, what is the new $x$-coordinate of the vertex originally at $(4, 1)$?

A point $K$ at $(3, -2)$ is rotated $90^{\circ}$ clockwise about the point $(1, -2)$. What are the new coordinates of point $K$?

A shape is composed of a semicircle with a diameter on the x-axis from $x=2$ to $x=6$. If this shape is reflected across the line $x=1$, what is the new interval for the diameter on the x-axis?

An architect is drawing a floor plan. Room A is a triangle with vertices $( -4, -1)$, $( -4, -3)$, and $( -1, -1)$. Room B is created by reflecting Room A across the x-axis and then reflecting the result across the y-axis. What is this combined transformation equivalent to?

A point $P$ is plotted on a coordinate grid as shown in the diagram. What are the coordinates of point $P$?

What is the $x$-coordinate of any point lying on the $y$-axis?

A rectangle has vertices at $(-1, 1), (3, 1), (3, -2)$ and $(-1, -2)$. What is the length of the side along the $x$-direction?

If point $F$ is at $(-1, 5)$, which movement describes getting there from the origin?

What shape is formed by connecting the points $(0, 2), (2, 0), (0, -2),$ and $(-2, 0)$ in order?

A line segment has an endpoint at $(-2, -2)$ and its midpoint at $(0, 0)$. What is the other endpoint?

Which of these points is closest to the $x$-axis?

Parallelogram $ABCD$ has vertices $A(-4, 1)$, $B(-1, 4)$, and $C(4, 4)$. What are the coordinates of vertex $D$?

A circle is centered at the origin $(0, 0)$ and has a radius of 5 units. Which of the following points lies exactly on the circumference of the circle?

A hiker is at point $X(-3, -4)$. He moves 6 units North and then 3 units East. What are his final coordinates?