Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Problems 1 to 7 use single steps and diagrams. Problems 8 to 14 introduce algebraic expressions. Problems 15 to 20 are multi-step word problems from construction, roads and signs.
Standards: 7.G.B.5 · Level: Grade 7
Problem 2 Find the supplement ★★★
Calculate the supplement of a 127° angle.
Problem 3 Vertical and adjacent ★★★
Two lines cross as shown. One angle measures 64°. Name the measure of the vertical angle and the measure of an adjacent angle.
Problem 4 Complementary equation ★★★
Two complementary angles measure x° and 41°. Write an equation and solve for x.
Problem 5 Straight line equation ★★★
The angles in the diagram lie on a straight line. Solve for x.
Problem 6 Four angles at a crossing ★★★
Lines cross and ∠1 = 72°. Find ∠2, ∠3 and ∠4.
Problem 7 Classify the pairs ★★★
Classify each pair of angle measures as complementary, supplementary, or neither. (a) 68° and 22°, (b) 99° and 81°, (c) 45° and 135°, (d) 30° and 50°.
Problem 8 Triple angle ★★★
Two supplementary angles are such that the larger is 3 times the smaller. Find both angles.
Problem 9 Complementary expressions ★★★
Two complementary angles measure (2x + 4)° and (x + 17)°. Find x and both angles.
Problem 10 Vertical angle expressions ★★★
In the figure, the vertical angles measure (4x − 12)° and (2x + 30)°. Find x and the angle measure.
Problem 11 Linear pair expressions ★★★
A linear pair has angle measures (6x − 5)° and (4x + 15)°. Find x and both angles.
Problem 12 Less than its complement ★★★
An angle measures 24° less than its complement. Find the angle.
Problem 13 More than its supplement ★★★
An angle measures 30° more than its supplement. Find the angle.
Problem 14 Three angles on a line ★★★
Three angles lie on a straight line as shown. Solve for x and find each angle.
Problem 15 Leaning ladder ★★★
A ladder leans against a vertical wall and makes a 74° angle with the level ground, as shown. Find the angle between the ladder and the wall, and the angle on the other side of the ladder with the ground.
Problem 16 Crossing roads ★★★
Two straight roads cross. One angle is (3x + 15)° and the angle vertical to it is (5x − 25)°. Find x, then all four angles at the crossing.
Problem 17 Split right angle ★★★
A laser beam OB splits a right-angle corner ∠AOC into ∠AOB = (5x + 4)° and ∠BOC = (4x + 14)°. Find x and both angles.
Problem 18 Supplement versus complement ★★★
Mia says that her mystery angle has a supplement four times as large as its complement. Set up an equation in one variable and find the mystery angle.
Problem 19 Bridge cables ★★★
Two steel cables on a bridge cross at a point. One angle between them is (7x − 4)° and the adjacent angle is (2x + 13)°. Find x and all four angles.
Problem 20 Sign board angle ★★★
A sign board is attached to a vertical post. The board makes an angle of (4x + 3)° with the horizontal ground line, and the angle between the board and the post is (x + 12)°. Find x and both angles.
