Testinar Grade 8 math

Angles in Triangles and Parallel Lines

Learn to reason about and solve Grade 8 problems involving Angles in Triangles and Parallel Lines.

CH05-05 Geometry and Measurement

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

In triangle \(ABC\), angle \(A\) measures 35° and angle \(C\) measures 62°. What is angle \(B\)?
1. 73°
2. 83°
3. 93°
4. 103°
In the diagram below, the exterior angle of a triangle measures 115°. If one remote interior angle is 48°, what is the other remote interior angle?
1. 50°
2. 60°
3. 67°
4. 115°
Two parallel lines are cut by a transversal. If one corresponding angle is 72°, what is the other corresponding angle?
1. 72°
2. 108°
3. 118°
4. 144°
In the diagram, lines \(\ell_1\) and \(\ell_2\) are parallel. Find the measure of angle \(x\).
1. 58°
2. 68°
3. 122°
4. 180°
Lines \(m\) and \(n\) are parallel, cut by a transversal. If one co-interior angle is 124°, what is the other co-interior angle?
1. 56°
2. 62°
3. 124°
4. 180°
In the figure, parallel lines are cut by a transversal. If the angle marked is 85°, find the alternate exterior angle.
1. 85°
2. 95°
3. 105°
4. 145°
A triangle has interior angles of 41° and 89°. What is the exterior angle adjacent to the third interior angle?
1. 50°
2. 100°
3. 130°
4. 180°
In the diagram, \(AB \parallel CD\). If angle \(1\) is 63° and angle \(2\) is 95°, what is angle \(3\)?
1. 22°
2. 32°
3. 42°
4. 52°

Teacher and parent reference

Answer key and explanations

B. 83°
Triangle angle sum: \(180 - 35 - 62 = 83°\).
C. 67°
An exterior angle equals the sum of the two remote interior angles: \(115 = 48 + x\), so \(x = 67°\).
A. 72°
Corresponding angles formed by parallel lines and a transversal are congruent.
A. 58°
Alternate interior angles formed by parallel lines and a transversal are congruent.
A. 56°
Co-interior angles (same-side interior angles) are supplementary: \(124 + y = 180\), so \(y = 56°\).
A. 85°
Alternate exterior angles are congruent when lines are parallel.
C. 130°
The third interior angle is \(180 - 41 - 89 = 50°\). The exterior angle is \(180 - 50 = 130°\) (or sum of remote interior angles: \(41 + 89 = 130°\)).
A. 22°
Angle 1 (63°) and angle 2 (95°) form a triangle with angle 3. The angle corresponding to angle 1 (by the parallel line property) is 63°. Then by triangle angle sum: angle 3 = \(180 - 63 - 95 = 22°\).