To find the measure of ∠B, we know that ∠A and ∠B are complementary angles. Complementary angles add up to 90°.
Also, ∠C is a straight angle, which measures 180°. ∠C is formed by the combination of ∠A and ∠B.
We are given that ∠C = 90°, so we can set up an equation to solve for x:
∠C = ∠A + ∠B
90° = x° + 2x°
90° = 3x°
Now, we can solve the equation for x:
3x° = 90°
x° = 90° / 3
x° = 30°
Since we have found the value of x, we can substitute it into the expression for ∠B:
∠B = 2x°
∠B = 2(30°)
∠B = 60°
Therefore, the measure of ∠B is 60°.
In a geometric diagram, ∠A and ∠B are complementary, and they form a straight line with ∠C . If m∠A=x° , m∠B=(2x)° , and m∠C=90° , what is the measure of ∠B ?
Responses:
90°
60°
30°
180°
1 answer
1 answer