This worksheet gives 20 problems on angle relationships, aligned with Common Core standard 7.G.B.5. The first problems ask for complements and supplements of given angles, and the middle problems use diagrams of crossing lines and angles on a line.
The last problems are word problems that need an equation with a variable, such as finding two supplementary angles when one is described in terms of the other. Work in order, and check each answer by adding the angles.
Problem 1: Complementary angles
Find the complement of each angle.
- \(22^{\circ}\)
- \(65^{\circ}\)
- \(81^{\circ}\)
Problem 2: Supplementary angles
Find the supplement of each angle.
- \(130^{\circ}\)
- \(77^{\circ}\)
- \(164^{\circ}\)
Problem 3: Find the missing angle
Solve each problem.
- Find the complement of \(53^{\circ}\).
- Find the supplement of \(146^{\circ}\).
- Find the measure of an angle that equals its own supplement.
Problem 4: Complementary or supplementary
Tell whether each pair of angles is complementary, supplementary, or neither.
- \(40^{\circ}\) and \(50^{\circ}\)
- \(110^{\circ}\) and \(70^{\circ}\)
- \(120^{\circ}\) and \(50^{\circ}\)
- \(25^{\circ}\) and \(155^{\circ}\)
Problem 5: Vertical angles
Two lines cross and one angle measures \(72^{\circ}\). Find the measures of angles \(a\), \(b\), and \(c\).
Problem 6: Crossing lines
Two lines cross and one angle measures \(125^{\circ}\). Find the measures of angles \(a\), \(b\), and \(c\).
Problem 7: Angles on a line
Find the value of \(x\).
Problem 8: Angles along a line
Three angles lie along a straight line. Find the value of \(x\).
Problem 9: Angles in a right angle
The corner of a square picture frame is split by a line. Find the value of \(x\).
Problem 10: Splitting a right angle
Two lines split the right angle of a drafting square into three angles. Find the value of \(x\).
Problem 11: Complementary equation
Two angles are complementary. One measures \(x^{\circ}\) and the other measures \((2x+9)^{\circ}\). Write an equation, solve for \(x\), and find both angle measures.
Problem 12: Supplementary equation
Two angles are supplementary. One measures \(x^{\circ}\) and the other measures \((x+36)^{\circ}\). Write an equation, solve for \(x\), and find both angle measures.
Problem 13: Vertical angles equation
Find \(x\) and \(y\).
Problem 14: Vertical angles with x
Two lines cross. The marked angles are vertical angles. (a) Find \(x\). (b) Find the measure of each marked angle. (c) Find the measure of an angle next to a marked angle.
Problem 15: Supplementary word problem
Two angles are supplementary. The larger angle is \(20^{\circ}\) more than 3 times the smaller angle. Write an equation and find both angles.
Problem 16: Complementary word problem
Two angles are complementary. One angle is \(12^{\circ}\) less than twice the other. Write an equation and find both angles.
Problem 17: Adjacent angles on a line
Two adjacent angles lie along a straight line. Find \(x\) and the measure of each angle.
Problem 18: Street corner
Oak Street and Pine Street cross. Two neighboring angles at the corner measure \((3x+5)^{\circ}\) and \((2x+25)^{\circ}\). Find \(x\) and the measures of all four angles at the corner.
Problem 19: Three angles on a line
Ethan folds a straight strip of paper twice. The three angles along the strip measure \(x^{\circ}\), \((x+10)^{\circ}\), and \((2x+10)^{\circ}\). Write an equation, solve for \(x\), and find all three angles.
Problem 20: Four angles on a line
Four angles lie along a straight line and measure \(x^{\circ}\), \((x+4)^{\circ}\), \((2x-8)^{\circ}\), and \((2x+16)^{\circ}\). Write an equation, solve for \(x\), and find the measure of each angle.
See every chapter on the Grade 7 math page.