Answer:
x= 12
Explanation:
∠QPR +∠PQR= ∠HRQ (ext. ∠ of △PQR)
30° +(4x +2)°= (8 +6x)°
32 +4x= 8 +6x (simplify)
Bring x terms on 1 side, constants to the other:
6x -4x= 32 -8
2x= 24 (simplify)
x= 24 ÷2 (÷2 on both sides)
x= 12
Method 2:
∠PRQ= 180° -30° -(4x +2)° (∠ sum of △PQR)
∠PRQ= (148 -4x)°
∠PRQ +∠HRQ= 180° (adj. ∠s on a str. line)
(148 -4x)° +(8 +6x)°= 180°
148 -4x + 8 +6x= 180
156 +2x= 180
2x= 180 -156
2x= 24
x= 24 ÷2
x= 12