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°.