Geometry

In the diagram, $ABC$ is a triangle and $BCD$ is a straight line. Given that $\angle BAC = 40^{\circ}$ and $\angle ABC = 85^{\circ}$, calculate the size of the exterior angle $x^{\circ}$.

Find the value of $z$ on the straight line.

In the triangle shown, the exterior angle is $130^\circ$ and one opposite interior angle is $50^\circ$. Find $x$.

A rectangle has a length of $10$ cm and a diagonal of $26$ cm. Find the width.

Determine the value of $x$ in the diagram, where the lines are tangents and radii of a circle.

In triangle $ABC$, the ratio of angles $A:B:C$ is $2:3:4$. Find the size of the largest angle.

Find the sum of the exterior angles of any convex decagon.

In triangle $LMN$, the bisectors of $\angle M$ and $\angle N$ meet at point $I$. If $\angle L = 80^{\circ}$, calculate the measure of $\angle MIN$.

An isosceles trapezium $ABCD$ has $AB$ parallel to $DC$. If $\angle ADC = 115^{\circ}$, calculate the size of $\angle ABC$.

Three lines intersect at a single point $O$. Two of the vertically opposite angles are labeled as $(4y - 12)^{\circ}$ and $(2y + 24)^{\circ}$. Find the value of $y$ and the size of one of the other four angles formed at the point.

Find the value of $x$ in the quadrilateral shown.

A square is rotated about its center. What is the smallest angle of rotation that maps the square onto itself?

If an exterior angle of a regular polygon is $20^{\circ}$, how many sides does it have?

Identify the number of lines of symmetry in a regular hexagon.

In the diagram, $ABCDE$ is a regular pentagon. $AFB$ is an equilateral triangle constructed inside the pentagon. Calculate the size of the angle $EAF$.

The exterior angles of a quadrilateral are in the ratio $1:2:3:4$. Find the largest interior angle of the quadrilateral.

A shape has rotational symmetry of order 4 and 4 lines of symmetry. Which of the following could it be?

In a convex polygon, four of the interior angles are $120^{\circ}$ each and the remaining interior angles are $160^{\circ}$ each. How many sides does this polygon have?

A decorative fence panel is in the shape of a regular decagon. To increase its height, a student adds a square to each side of the decagon. If the student then connects the outer corners of these squares to form a new polygon, how many sides does the new outer polygon have?

A regular polygon has an interior angle that is $140^{\circ}$ greater than its exterior angle. Find the number of sides of this polygon.

What is the angle between a radius and a tangent at the point of contact?

In the diagram, $O$ is the center and $\angle OAB = x$. Find $\angle OBA$.

If $\angle ADC = 115^\circ$ in cyclic quadrilateral $ABCD$, find the exterior angle at $B$.

In the diagram, $\angle BAC = 35^\circ$. What is the size of $\angle BOC$ at the center?

In the diagram, $PQ$ is a diameter. $\angle RPQ = 30^\circ$. Find $\angle RQP$.

In the diagram, $O$ is the center. $\angle ABC = 125^\circ$. Find $\angle ADC$ where $D$ is on the major arc.

Two circles touch externally. The radius of the first circle is $9$ cm and the radius of the second circle is $4$ cm. Find the length of the common tangent $AB$.

In a design, two points $E$ and $F$ lie on a circle with center $O$. A tangent is drawn at $E$. A point $G$ is chosen on the circumference such that $\angle OEF = 25^{\circ}$. Find the angle $\angle EGF$ subtended by the chord $EF$ at the circumference.

A circular tunnel is reinforced with a horizontal cross-beam $AB$ that is $16$ m long. The distance from the center of the tunnel $O$ to the midpoint of the beam $M$ is $6$ m. Calculate the radius of the tunnel.

A ferris wheel has seats at points $L, M, N$ on its circumference. $O$ is the center. If the central angle $\angle LON = 150^{\circ}$, what is the angle $\angle LMN$ subtended at seat $M$ on the major arc?

If $\triangle ABC \cong \triangle FED$ by RHS rule, and $BC = 5$ cm, $AC = 13$ cm, which side in $\triangle FED$ is $12$ cm long?

Which of the following conditions is NOT sufficient for two triangles to be congruent?

In the diagram, $\triangle ABC \cong \triangle DEF$. If $\angle A = 50^\circ$ and $\angle E = 60^\circ$, what is the measure of $\angle C$?

Identify the reason why triangle $ABC$ is congruent to triangle $CDA$ in the given rectangle $ABCD$.

A $2$ m tall man stands $10$ m away from a lamp post. If his shadow is $4$ m long, what is the height of the lamp post?

In the diagram, $\triangle PQR$ is similar to $\triangle RST$. If $PQ = 5$, $QR = 12$, $PR = 13$, and $RS = 24$, what is the length of $ST$?

Two similar prisms have surface areas of $50$ cm$^2$ and $200$ cm$^2$. If the volume of the smaller prism is $30$ cm$^3$, what is the volume of the larger prism?

Two triangles $ABC$ and $PQR$ are similar. The ratio of their corresponding sides is $k:1$. If the area of $\triangle ABC$ is $50$ cm$^2$ and the area of $\triangle PQR$ is $18$ cm$^2$, find the value of $k$.

In the circle shown, chords $AB$ and $CD$ intersect at point $E$ inside the circle. If $AE = 8$ cm, $EB = 6$ cm, and $DE = 4$ cm, find the length of $EC$.

A map is drawn to a scale of $1:50,000$. A forest is represented by a region with an area of $12$ cm$^2$ on the map. Calculate the actual area of the forest in square kilometers ($1$ km$^2 = 10^{10}$ cm$^2$).

1. Geometrical Terms: practice question 1 for Geometry?

1. Geometrical Terms: practice question 2 for Geometry?

1. Geometrical Terms: practice question 3 for Geometry?

1. Geometrical Terms: practice question 4 for Geometry?

1. Geometrical Terms: practice question 5 for Geometry?

1. Geometrical Terms: practice question 6 for Geometry?

1. Geometrical Terms: practice question 7 for Geometry?

1. Geometrical Terms: practice question 8 for Geometry?

1. Geometrical Terms: practice question 9 for Geometry?

1. Geometrical Terms: practice question 10 for Geometry?

1. Geometrical Constructions: practice question 1 for Geometry?

1. Geometrical Constructions: practice question 2 for Geometry?

1. Geometrical Constructions: practice question 3 for Geometry?

1. Geometrical Constructions: practice question 4 for Geometry?

1. Geometrical Constructions: practice question 5 for Geometry?

1. Geometrical Constructions: practice question 6 for Geometry?

1. Geometrical Constructions: practice question 7 for Geometry?

1. Geometrical Constructions: practice question 8 for Geometry?

1. Geometrical Constructions: practice question 9 for Geometry?

1. Geometrical Constructions: practice question 10 for Geometry?

1. Scale Drawings: practice question 1 for Geometry?

1. Scale Drawings: practice question 2 for Geometry?

1. Scale Drawings: practice question 3 for Geometry?

1. Scale Drawings: practice question 4 for Geometry?

1. Scale Drawings: practice question 5 for Geometry?

1. Scale Drawings: practice question 6 for Geometry?

1. Scale Drawings: practice question 7 for Geometry?

1. Scale Drawings: practice question 8 for Geometry?

1. Scale Drawings: practice question 9 for Geometry?

1. Scale Drawings: practice question 10 for Geometry?