Question

If mangle upper A upper O upper C= 85°, mangle upper B upper O upper C = 2x + 10, and mangle upper A upper O upper B = 4x – 15, find the degree measure of angle upper B upper O upper Cand angle upper A upper O upper B

Answer 1

To find the degree measure of angle BOC, we can use the fact that the sum of the interior angles of a triangle is 180°. Since angle AOC and angle AOB are known, we can find angle BOC.

Given:
angle AOC = 85°,
angle AOB = 4x - 15°

Since the sum of the interior angles of a triangle is 180°, we have:
angle BOC + angle AOC + angle AOB = 180°

Substituting the given values:
angle BOC + 85° + (4x - 15°) = 180°

Simplifying the equation:
angle BOC + 4x + 70° = 180°
angle BOC + 4x = 110°

Now, we are given that angle BOC = 2x + 10°, so:
2x + 10° + 4x = 110°

Combining like terms:
6x + 10° = 110°

Subtracting 10° from both sides:
6x = 100°

Dividing by 6:
x = 100° / 6
x = 16.67° (rounded to the nearest hundredth)

Now we can find the degree measure of angle BOC using the value of x we just obtained:
angle BOC = 2x + 10°
angle BOC = 2(16.67°) + 10°
angle BOC = 33.33° + 10°
angle BOC = 43.33°

Therefore, angle BOC measures approximately 43.33°.

To find the degree measure of angle AOB, we can substitute the value of x into the given expression:
angle AOB = 4x - 15°
angle AOB = 4(16.67°) - 15°
angle AOB = 66.67° - 15°
angle AOB = 51.67°

Therefore, angle AOB measures approximately 51.67°.