Lines and Angles

Identify the type of angle shown in the figure.

Find $x$ in the figure if $m \parallel n$.

If two parallel lines are intersected by a transversal, then each pair of alternate interior angles is:

Which of the following describes a reflex angle?

In the given figure, $AB \parallel CD$. If $\angle APQ = 50^\circ$ and $\angle PRD = 127^\circ$, find the value of $y$ where $y$ is the measure of $\angle QPR$.

In the figure, lines $XY$ and $MN$ intersect at $O$. If $\angle POY = 90^\circ$ and $a : b = 2 : 3$, find the value of $c$.

In the given figure, $POQ$ is a straight line. Ray $OR$ is perpendicular to line $PQ$. Ray $OS$ is another ray lying between rays $OP$ and $OR$. If $\angle ROS = 25^\circ$, find the measure of $\angle POS$.

In a crystal lattice structure, two planes are represented by parallel lines $L_1$ and $L_2$. A transversal $T$ makes an angle of $105^\circ$ with $L_1$. If a perpendicular is dropped from a point on $L_1$ to $L_2$, what is the angle between the transversal $T$ and the perpendicular?

A drafting student is told that for two lines $m$ and $n$, the interior angles on the same side of a transversal $p$ are $(x+30)^\circ$ and $(2x+60)^\circ$. What value of $x$ would make $m$ and $n$ parallel?

In a road intersection diagram, line $AB \parallel CD$. Transversal $PQ$ intersects $AB$ at $R$ and $CD$ at $S$. If $\angle ARS = 5x + 20^\circ$ and $\angle DSR = 2x + 10^\circ$, find the value of $\angle BRS$.

In the given figure, lines $AB$ and $CD$ intersect at point $O$. If $\angle AOC + \angle BOE = 70^{\circ}$ and $\angle BOD = 40^{\circ}$, find the value of $\angle BOE$.

In the figure, if $l \parallel m$, find the value of $x$.

The angle which is equal to eight times its complement is:

If $\angle 1$ and $\angle 2$ are supplementary angles and $\angle 1 = 2\angle 2$, find $\angle 1$.

In the given figure, three lines $l$, $m$, and $n$ intersect at a single point $O$. Based on the relationship of vertically opposite angles and angles on a straight line, what is the value of $x$?

In the figure, lines $XY$ and $MN$ intersect at $O$. If $\angle POY = 90^{\circ}$ and $a : b = 2 : 3$, find the measure of angle $c$.

If two parallel lines are intersected by a transversal, the bisectors of any two corresponding angles are:

In a decorative pattern, two lines $AB$ and $CD$ intersect at $O$. If $\angle AOC = (3x + 10)^\circ$ and $\angle AOD = (2x - 30)^\circ$, find the value of $x$ that makes these angles a linear pair.

On a construction site, three lines $l, m, n$ are such that $l \parallel m$ and $m \parallel n$. If the transversal $t$ intersects them and the ratio of interior angles on the same side between $l, m$ and $m, n$ is $4:5$, find the measure of the smaller interior angle if they are consecutive interior angles between the same pair of parallels.

Two straight lines $AB$ and $CD$ intersect at $O$. If $\angle AOC + \angle COB + \angle BOD = 280^\circ$, determine the measure of $\angle AOC$.

In the figure, if $m || n$ and $\angle 1 = 65^\circ$, find $\angle 5$.

If $\angle 1$ and $\angle 2$ are vertically opposite angles, then $\angle 1 = 60^\circ$ implies $\angle 2$ is:

The sum of all angles around a point is:

If a transversal intersects two parallel lines, then which of the following is NOT necessarily true?

In the figure, if $AB || CD || EF$ and $y:z = 3:7$, find $x$.

If an angle is five times its complement, find the angle.

In the given figure, $AB || CD$. Find the value of $x$.

Lines $AB$ and $CD$ intersect at $O$. If $\angle AOC + \angle BOD = 140^\circ$, find the value of $\angle AOD$.

Two intersecting lines form four angles. If one of the angles is thrice the size of its neighbor, what is the measure of the largest angle formed at the intersection?

A surveyor marks two lines $AB$ and $CD$ intersecting at $O$. If $\angle AOC + \angle COE = 180^\circ$, and $\angle COE$ and $\angle EOB$ are in the ratio $2:1$, and $AB$ is a straight line, what is the measure of $\angle EOB$ if $\angle AOC = 60^\circ$?

If $\angle 3$ and $\angle 6$ are interior angles on the same side of a transversal and $\angle 3 = x + 20$ and $\angle 6 = x - 10$, for what value of $x$ are the lines parallel?

If line $m \parallel n$ and $\angle 1 = 60^\circ$, find $\angle 8$ (alternate exterior angle).

If a transversal intersects two lines such that a pair of alternate interior angles are equal, then the two lines are:

Find the value of $x$ if $L_1 \parallel L_2$.

In the given figure, line $AB$ is parallel to line $CD$ ($AB \parallel CD$). A transversal $l$ intersects $AB$ at $P$ and $CD$ at $Q$. If $\angle APQ = (3x + 10)^\circ$ and $\angle PQC = (2x + 20)^\circ$, what is the value of $x$?

Find the value of $x$ if $AB \parallel CD$ and $CD \parallel EF$. Given $\angle ABC = 70^\circ$ and $\angle CEF = 130^\circ$.

In the figure, $l \parallel m$ and $n$ is a transversal. If $\angle 1 : \angle 2 = 5 : 4$, find $\angle 1$. Note: $\angle 1$ and $\angle 2$ are co-interior angles.

A light ray $PQ$ strikes a mirror $AB$ at $Q$, reflects as $QR$, and then reflects off mirror $BC$ at $R$. If $AB \parallel CD$ and the mirrors $AB$ and $BC$ are arranged such that $BC$ is a transversal, and the angle of incidence at $Q$ is $40^\circ$, and $\angle QRC = 100^\circ$, what is the angle between the mirrors $AB$ and $BC$?

In a truss for a roof, the top chord $AC$ and bottom chord $DF$ are parallel. The vertical member $BE$ connects them. If a diagonal member $AF$ is drawn such that $\angle CAF = 30^\circ$ and another diagonal $CD$ is drawn such that $\angle ACD = 45^\circ$, what is the angle between the two diagonals if they intersect at a point $O$?

In the given figure, $AB \parallel CD$ and $CD \parallel EF$. Also $EA \perp AB$. If $\angle BEF = 55^\circ$, find the value of $\angle EAB + \angle ABD$ (if $D, B$ and $F$ are vertices of the angles formed by a transversal). More specifically, find the angle $x$ where $x = \angle ACE$ given the configuration.