Lines and Angles

Find the supplement of $105^{\circ}$.

Two angles are such that they have a common vertex, a common arm, but no common interior points. They are called:

In a linear pair, if one angle is acute, the other angle must be:

What is the complement of $56^{\circ}$?

Two supplementary angles differ by $40^{\circ}$. Find the smaller angle.

In the following figure, $\angle 1 = 3x$ and $\angle 2 = 2x + 30^{\circ}$. Find $x$ if they form a linear pair.

If an angle is double its complement, what is the measure of the angle?

An architect is designing a section of a bridge where two steel girders cross each other as shown in the diagram. He knows that the angle marked as $\angle 1$ and the angle marked as $\angle 2$ are vertically opposite. If $\angle 1 = (3x + 10)^\circ$ and the angle adjacent to it, $\angle 3$, forms a linear pair such that $\angle 3 = (2x + 20)^\circ$, find the measure of the vertically opposite angle $\angle 2$.

Find the value of an angle which is half of its own complement.

If the difference between two supplementary angles is $30^\circ$, find the ratio of the smaller angle to the larger angle.

In the given figure, lines $l$ and $m$ are parallel ($l \parallel m$) and line $t$ is a transversal. If $\angle 1 = 110^{\circ}$, what is the measure of $\angle 2$?

If two lines are parallel, the distance between them:

In the figure, $\angle 4$ and $\angle 6$ are known as:

When two lines intersect, if one angle is $90^\circ$, then the other three angles are each:

In the figure, find $x$ if $m \parallel n$.

Identify the value of $a$ if the lines $l$ and $m$ are parallel.

In the figure, if $AB \parallel CD$, find the value of $x$.

Line $A$ is parallel to line $B$. Line $C$ is a transversal. One exterior angle is $x$ and its alternate exterior angle is $y$. If $x = 2z + 10$ and $y = z + 40$, find the value of $z$.

If two parallel lines are cut by a transversal, and one of the interior angles is $115^{\circ}$, find the difference between the largest and smallest angles formed at the intersections.

A window frame has two horizontal bars that are parallel. A decorative diagonal bar makes an angle of $55^{\circ}$ with the top bar. What is the measure of the obtuse angle it makes with the bottom bar on the same side of the diagonal?

What is the name for the line that intersects two or more lines at distinct points?

If $\angle 1 = 75^{\circ}$ and $\angle 1$ and $\angle 5$ are corresponding angles for parallel lines, then $\angle 5$ is:

In the given diagram, $\angle 1$ and $\angle 2$ are:

Which of these pairs represents alternate exterior angles?

In the given figure, line $l$ is parallel to line $m$ ($l \parallel m$) and line $n$ is a transversal. If one of the interior angles on the same side of the transversal is $(3x + 10)^{\circ}$ and the other is $(2x + 20)^{\circ}$, what is the value of $x$?

In the diagram, if line $a \parallel b$ and line $c \parallel d$, and $\angle 1 = 70^{\circ}$, what is the value of $\angle 2$?

Find $x$ if $l \parallel m$. The interior angles on the same side of the transversal are $(3x + 20)^{\circ}$ and $(x - 40)^{\circ}$.

A designer creates a pattern with parallel lines $L_1$ and $L_2$. A transversal $T$ forms an exterior angle of $130^{\circ}$. What is the measure of the interior angle on the same side of the transversal that is NOT adjacent to the corresponding interior angle?

Two stripes on a shirt are parallel. A thread crosses them at an angle. If the corresponding angles are $(4k - 12)^{\circ}$ and $(2k + 28)^{\circ}$, find the angle measure.

A shelf unit has parallel shelves. A support bar crosses them. If the alternate interior angles are $(2a + 10)^{\circ}$ and $(3a - 20)^{\circ}$, what is the value of $a$?

In the diagram, if line $m \parallel n$, what is the sum of angles 1 and 2?

If $\angle a$ and $\angle b$ are interior angles on the same side of a transversal and $\angle a = 80^\circ, \angle b = 100^\circ$, what is the relationship between the lines?

In the figure, if $x = 100^\circ$ and $y = 100^\circ$, then line $L$ is parallel to line $M$ because:

If $\angle 1$ and $\angle 2$ are alternate exterior angles and $\angle 1 = \angle 2$, then the lines are parallel. Is this statement true?

If two lines are parallel to the same line, then they are parallel to each other. This is a property used to check for parallelism. If $l \parallel n$ and $m \parallel n$, then:

Find $y$ such that line $AB \parallel CD$. Given $\angle AGE = (2y + 20)^\circ$ and $\angle CHG = 80^\circ$ (where $EF$ is the transversal and $G, H$ are intersection points).

In the figure, if $\angle 1 = 75^\circ$, find the value of $\angle 2$ such that line $l \parallel m$.

A shelf bracket system uses two parallel vertical supports. A diagonal brace is attached such that the alternate interior angles are $(2x + 10)^{\circ}$ and $(3x - 20)^{\circ}$. What value of $x$ ensures the vertical supports are perfectly parallel?

A solar panel array has two support rails. A crossbar makes an angle of $110^{\circ}$ with the top rail (exterior angle). For the rails to be parallel, what must be the measure of the interior angle on the opposite side (alternate exterior) of the crossbar at the bottom rail?

In a patterned fabric, two stripes $S_1$ and $S_2$ are crossed by a thread $T$. The corresponding angles are $(3x + 15)^{\circ}$ and $(2x + 30)^{\circ}$. If the stripes are parallel, find the actual measure of these corresponding angles.