Question

In triangle XYZ, the measure of angle X is 84, the measure of angle Y is (r + 59) and the measure of angle z is (r + 51), find the value of r and the measure of angle Y.

Answer 1

• r = -7
• Y = 52°

Explanation:

The sum of the measures of the angles in a triangle is 180°.

X + Y + Z = 180°

84° +(r +59)° +(r +51)° = 180°

2r +194 = 180 . . . . . . . . . divide by ° and simplify

2r = -14 . . . . . . . . . . subtract 194

r = -7

Then the measure of Y is ...

Y = (r +59)° = (-7 +59)°

Y = 52°

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Additional comment

Z = 44°