Question

Measures of each interior angle

Answer 1

Given:

∠Q = (2x + 5)°, ∠R = x°

∠S = (2x + 7)°, ∠T = x°

To find:

The measure of each interior angle.

Solution:

Sum of all the angles of a quadrilateral = 360°

∠Q + ∠R + ∠S + ∠T = 360°

2x° + 5° + x° + 2x° + 7° + x° = 360°

6x° + 12° = 360°

Subtract 12° from both sides.

6x° = 348°

Divide by 6 on both sides.

x° = 58°

The measure of angle R is 58°.

The measure of angle T is 58°.

Substitute x = 58 in Q, and S.

∠Q = (2(58) + 5)°

     = (116 + 5)°

∠Q = 121°

The measure of angle Q is 121°.

∠T = (2(58) + 7)°

     = (116 + 7)°

∠T = 123°

The measure of angle T is 123°.