Problem Set: Angle Relationships in Triangles and Parallel Lines - Grade 8

Question 1

In triangle ABC, the measure of angle A is $52^\circ$ and the measure of angle B is $71^\circ$. Find the measure of angle C, labeled $x$. Figure: Triangle ABC with angle A marked 52 degrees, angle B marked 71 degrees, and angle C marked x. — angle A = 52°, angle B = 71°, angle C = x

Accepted Answer

$x = 57^\circ$

Question 2

In triangle PQR, angle P measures $(2x + 10)^\circ$, angle Q measures $(3x - 5)^\circ$, and angle R measures $(x + 25)^\circ$. Find $x$ and the measure of each angle.

Accepted Answer

$x = 25$; angle P = $60^\circ$, angle Q = $70^\circ$, angle R = $50^\circ$

Question 3

In triangle DEF, side DF is extended past F to point G. The remote interior angles measure $48^\circ$ (angle D) and $65^\circ$ (angle E). Find the measure of exterior angle EFG.

Accepted Answer

$113^\circ$

Question 4

An exterior angle of a triangle measures $(5x + 4)^\circ$. The two remote interior angles measure $(2x + 10)^\circ$ and $(x + 30)^\circ$. Find $x$ and the measure of the exterior angle.

Accepted Answer

$x = 18$; exterior angle = $94^\circ$

Question 5

Lines $m$ and $n$ are parallel and are cut by a transversal $t$. One angle formed measures $(4x - 12)^\circ$, and its alternate interior angle measures $(2x + 36)^\circ$. Find $x$ and the measure of each angle.

Accepted Answer

$x = 24$; each angle measures $84^\circ$

Question 6

Lines $p$ and $q$ are parallel and are cut by a transversal. Two same-side interior angles measure $(3x + 15)^\circ$ and $(2x + 40)^\circ$. Find $x$ and the measure of each angle.

Accepted Answer

$x = 25$; the angles measure $90^\circ$ and $90^\circ$

Question 7

Line $\ell$ passes through vertex B of triangle ABC and is parallel to side AC. The angle between line $\ell$ and side BA (on the side near A) measures $58^\circ$, and the angle between line $\ell$ and side BC (on the side near C) measures $47^\circ$. Use alternate interior angles to find the measures of angles A, B, and C of the triangle.

Accepted Answer

angle A = $58^\circ$, angle C = $47^\circ$, angle B = $75^\circ$

Question 8

Two parallel lines are cut by two transversals that meet at point K, forming triangle JKL with J and L on the bottom parallel line. On the top parallel line at K, the angle to the left of segment KJ measures $64^\circ$ and the angle to the right of segment KL measures $55^\circ$. Find the measure of angle JKL.

Accepted Answer

$61^\circ$

Question 9

Lines $a$ and $b$ are parallel. A transversal crosses them, forming a corresponding angle pair. On line $b$, one of these corresponding angles, $(6x - 20)^\circ$, is also an interior angle of a triangle whose other two interior angles measure $40^\circ$ and $(2x + 12)^\circ$. The corresponding angle on line $a$ measures $70^\circ$. Find $x$, and check that the triangle's angles add to $180^\circ$.

Accepted Answer

$x = 15$; triangle angles $70^\circ$, $40^\circ$, $42^\circ$ do not add to $180^\circ$

Question 10

In triangle XYZ, angle X measures $35^\circ$. Side YZ is extended past Z, and the exterior angle at Z measures $110^\circ$. Find the measure of angle Y and the measure of interior angle Z.

Accepted Answer

angle Y = $75^\circ$, angle Z = $70^\circ$

Problem Set: Angle Relationships in Triangles and Parallel Lines - Grade 8

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