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

30°
30 degrees

60°
60 degrees

90°

Answer 1

Given that angles ∠A and ∠B are complementary, we know that:

\[ m∠A + m∠B = 90° \]

You're also given that \( m∠A = x° \) and \( m∠B = 2x° \).

Substituting these values into the equation gives us:

\[ x + 2x = 90° \]

This simplifies to:

\[ 3x = 90° \]

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

\[ x = 30° \]

Now, to find the measure of angle B:

\[ m∠B = 2x = 2(30°) = 60° \]

Therefore, the measure of \( m∠B \) is 60°.