In a geometric diagram, ∠A

Question

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
?(1 point)
Responses

180°
180 degrees

90°
90 degrees

60°
60 degrees

30°
30 degrees

Answer 1

Since angles A and B are complementary, we have:

\[ m∠A + m∠B = 90° \]

Given:

\[ m∠A = x° \quad \text{and} \quad m∠B = (2x)° \]

Substituting these values into the relationship for complementary angles, we get:

\[ x + 2x = 90° \]

This simplifies to:

\[ 3x = 90° \]

Now, solving for \(x\):

\[ x = \frac{90°}{3} = 30° \]

Now, we can find the measure of angle B:

\[ m∠B = 2x = 2(30°) = 60° \]

So, the measure of angle B is:

60°.