To find the measure of ∠B, we can add the measures of ∠A and ∠C, and then subtract the sum from 180°.
Given:
m∠A = 67°
m∠C = x°
So, ∠A + ∠C = 67° + x°.
∠B = (2x + 20)°.
Since the measures of the three angles add up to 180°,
67° + x° + (2x + 20)° = 180°.
Combining like terms,
67° + 20° + x° + 2x° = 180°.
Simplifying the expression,
(x + 2x)° + (67° + 20°) = 180°.
Combining like terms,
3x + 87° = 180°.
Subtracting 87 from both sides,
3x = 93°.
Dividing both sides by 3,
x = 31°.
So, the measure of ∠B is 2x + 20° = 2(31°) + 20° = 62° + 20° = 82°.
Therefore, the measure of ∠B is 82°.
The correct answer is A. 82.
There are angles whose measures add to 180° . Their measures are: m∠A=67°, m∠B=(2x+20)°, and m∠C=x°. What is the measure of ∠B?
A. 82
B. 62
C. 180
D. 31
1 answer