Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Mark each known angle on a sketch and name the relationship before solving.
Standards: 8.G.A.5 · Level: Grade 8
Problem 2 Right triangle ★★★
One acute angle of a right triangle is 37°. Find the other acute angle.
Problem 3 Isosceles apex ★★★
An isosceles triangle has a vertex angle of 40°. Find each base angle.
Problem 4 Exterior angle ★★★
The remote interior angles of a triangle measure 52° and 64°. Find the exterior angle at the third vertex.
Problem 5 Vertical and adjacent ★★★
Two lines cross. One angle measures 128°. Find the vertical angle and the angle adjacent to it.
Problem 6 Corresponding angles ★★★
In the figure, ℓ ∥ m. Find x and name the angle relationship.
Problem 7 Alternate interior ★★★
In the figure, ℓ ∥ m. Find y.
Problem 8 Same-side interior ★★★
Two parallel fence rails are crossed by a brace. A same-side interior angle measures 143°. Find the other one.
Problem 9 Triangle with x ★★★
The angles of a triangle measure (x + 10)°, (2x − 5)°, and (3x + 13)°. Find x and each angle.
Problem 10 Exterior with x ★★★
An exterior angle of a triangle measures (5x − 12)°. The remote interior angles measure (x + 20)° and (2x + 10)°. Find x and the exterior angle.
Problem 11 Parallel with x ★★★
A transversal crosses two parallel lines, and a pair of corresponding angles measures (3x + 8)° and (5x − 22)°. Find x and the angle measure.
Problem 12 Same-side with x ★★★
A transversal crosses two parallel lines, and the same-side interior angles measure (7x − 5)° and (3x + 15)°. Find x and both angles.
Problem 13 All eight angles ★★★
In the figure, ℓ ∥ m. Find the measure of each numbered angle.
Problem 14 Parallel or not? ★★★
Decide whether lines ℓ and m must be parallel. (a) A transversal makes corresponding angles of 67° and 69°. (b) A transversal makes alternate interior angles of 81° and 81°. Explain each answer.
Problem 15 AA similarity ★★★
Triangle ABC has angles of 44° and 79°. Triangle DEF has angles of 79° and 57°. Are the triangles similar? Justify your answer.
Problem 16 Roof truss ★★★
A roof truss is an isosceles triangle with a 104° angle at the peak. Find each base angle where the truss meets the wall plate.
Problem 17 Parallel streets ★★★
Elm Street and Oak Street are parallel, and a straight avenue crosses both. At Elm Street, the angle between the avenue and the street on the upper right measures 123°. Find the angle y on the lower left at Oak Street, and explain your reasoning.
Problem 18 Garden angles ★★★
The angles of a triangular garden are in the ratio 3 : 4 : 5. Find each angle.
Problem 19 Find the interior angle ★★★
In △ABC, ∠A = (2x + 3)° and ∠B = (3x − 7)°. The exterior angle at C measures (7x − 20)°. Find x and the interior angle at C.
Problem 20 Why 180? ★★★
A line through vertex B of △ABC is drawn parallel to side AC. The angles it makes with BA and BC measure 47° and 68°, and they are alternate interior angles with ∠A and ∠C. Find ∠ABC and explain why the three angles of the triangle total 180°.
