Question

Please help with this question ​

Answer 1

Step-by-step explanation:

m< AOC = 90°

m< AOB +m<BOC = 90°

6x-12+3x +30 = 90°

9x +18° = 90°

9x = 90- 18° = 72°

x = 8°

m<AOB =6(8)-12 = 48-12 = 36°

Answer 2

Since, OA is perpendicular to OC

$m\angle A OC= 90 \degree \\ m\angle AOB \: + m\angle BOC = 90 \degree \\ (6x - 12) \degree + (3x + 30) \degree = 90 \degree \\ 6x + 3x + 30 - 12 = 90 \degree \\ 9 x + 18 = 90 \\ 9x = 90 - 18 \\ 9x = 72 \\ x = \frac{72}{9} \\ x = 8 \degree$

$m\angle \: AOB = 6x - 12 \\ m\angle \: AOB = 6(8) - 12 \\ m\angle \: AOB = 48 - 12 \\ m\angle \: AOB = 36 \degree$