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Unknown Angles Equations

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Unknown Angles Equations

Use angle relationships to write an equation, solve it, and check that your angle measures make sense. Angles are measured in degrees.

Use angle relationships

Show your equation and working for each question.

1.Two adjacent angles make a straight line. Their measures are 4x° and (x + 30)°. Find x.

2.A pair of vertically opposite angles measure (3y − 18)° and (y + 26)°. Work out y.

3.Two angles add to 90°. Their measures are 5a° and (a + 18)°. Find a and the size of each angle.

4.Four angles around a point are x°, (2x + 15)°, 75° and 60°. Find x.

Solve and check

Use the stated angle relationship to form an equation. Include angle sizes when asked.

5.Two intersecting lines form vertically opposite angles of (4x + 5)° and (6x − 35)°. Find x, then state the sizes of all four angles.

6.Two supplementary angles are (3x + 20)° and (2x + 10)°. Find x and both angle measures.

7.Three adjacent angles lie on a straight line. They measure x°, (3x − 10)° and (x + 20)°. Find x and check the three angles total 180°.

Challenge and explain

Use algebra and angle facts carefully. Give clear reasoning.

8.Two supplementary angles are written as 2(2x + 5)° and 3(x + 10)°. Expand the brackets, solve for x, then find both angles.

9.At the school canteen, Tui sketches two intersecting lines. One pair of vertically opposite angles is labelled (5p + 8)° and (3p + 40)°. Find p and the size of each of the four angles.

10.Explain why vertically opposite angles are set equal, while adjacent angles on a straight line are added to make 180°. Include one simple algebraic example of each relationship.