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Solving Unknown Angles Algebraically

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Solving Unknown Angles Algebraically

Use angle facts to write an equation, solve for the variable, and then find any requested angle measures. Show your working and include degree symbols in your answers.

Angle relationships and equations

1.Two angles on a straight line measure (2x + 18)° and (x + 36)°. What is x?

2.Two vertically opposite angles are (3y − 12)° and (y + 28)°. Find y and the measure of each of these angles.

3.Two complementary angles are in the ratio 4:5. Let the smaller angle be 4n° and the larger angle be 5n°. Write an equation and find n and both angles.

4.Three adjacent angles on a straight line are (x + 12)°, (2x − 6)°, and (x + 18)°. Find x and the size of each angle.

Solve using more than one angle fact

5.Angles around a point are 2a°, (a + 24)°, (2a − 6)°, and 54°. Find a and the four angle measures.

6.Two intersecting lines form a pair of vertically opposite angles measuring (5m + 8)° and (3m + 36)°. Find m, then give the measures of all four angles.

7.The interior angles of a triangle are (p + 9)°, (2p − 3)°, and (3p + 6)°. Find p and all three angle measures.

8.Which equation correctly represents two adjacent angles on a straight line measuring (4x − 10)° and (2x + 16)°?

(4x − 10) + (2x + 16) = 90
(4x − 10) + (2x + 16) = 180
(4x − 10) = (2x + 16)
(4x − 10) + (2x + 16) = 360

9.Match each angle relationship to the total or equality you would use to form an equation.

Angles on a straight line
Angles around a point
Vertically opposite angles
Angles in a triangle
Complementary angles
Supplementary angles

Are equal
Add to 180°
Add to 90°
Add to 180°
Add to 360°
Add to 180°

Explain your reasoning

10.A straight-line pair of angles measures (3t + 15)° and (t + 45)°. Write an equation, solve for t, and explain which angle fact makes your equation valid.

11.A learner says vertically opposite angles must each be 90°. Is that always true? Use an example of intersecting lines with one angle measuring 68° to justify your answer, and state the measures of the other three angles.