Answer:
9. 75°
10. 60°
Explanation:
Note the angle-intercept theorem. If you create an angle in the opposite side of a circle from 2 points on other side, the arc will have a measure TWICE that of the intercepted angle created on other side.
Question 9
Arc WX has a measure 76, thus the angle created is Angle V, which should be HALF of that. So angle V is 76/2 = 38
Now looking at the triangle inside the circle, we know three angles of a triangle add up to 180, thus we can write and solve for "?" angle:
X + W + V = 180
? + 67 + 38 = 180
? + 105 = 180
? = 180 - 105 = 75°
Question 10
Using the theorem we can say that Angle B is HALF of ARC XYZ.
So,
2*Angle B = Arc XY + Arc YZ
2*102 = Arc XY + 124
204 = Arc XY + 124
Arc XY = 204 - 124 = 80°
Also, Arc BX + Arc XY is twice that of Angle Z (which is 70), thus
Arc BX + Arc XY = 70 *2
Arc BX + Arc XY = 140
Arc BX + 80 = 140
Arc BX = 140 - 80 = 60°