Question

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
?(1 point)
Responses

90°
90 degrees

180°
180 degrees

30°
30 degrees

60°
60 degrees

Answer 1

Since angles A and B are complementary, we have:

\[
m∠A + m∠B = 90°
\]

We know that:

\[
m∠A = x°
\]
\[
m∠B = 2x°
\]

Substituting the expressions into the equation gives:

\[
x + 2x = 90°
\]

This simplifies to:

\[
3x = 90°
\]

To find \(x\), divide both sides by 3:

\[
x = 30°
\]

Now we can find the measure of \(∠B\):

\[
m∠B = 2x = 2(30°) = 60°
\]

Therefore, the measure of \(∠B\) is:

\[
\boxed{60°}
\]