Question

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

60°
60 degrees

30°
30 degrees

90°
90 degrees

180°

Answer 1

Since angles A and B are complementary, we know that:

\[ m∠A + m∠B = 90° \]

Given that \( m∠A = x° \) and \( m∠B = 2x° \), we can substitute these expressions into the equation:

\[ x + 2x = 90° \]

This simplifies to:

\[ 3x = 90° \]

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

\[ x = 30° \]

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

\[ m∠B = 2x = 2 \cdot 30° = 60° \]

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