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

30°
30 degrees

90°
90 degrees

180°
180 degrees

60°

Answer 1

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

\[ m∠A + m∠B = 90° \]

It is also given that:

• \( m∠A = x° \)
• \( m∠B = 2x° \)
• \( m∠C = 90° \) (but this is already used in the definition of complementary angles)

Substituting the expressions for ∠A and ∠B into the complementary angle equation gives:

\[ x + 2x = 90° \]

This can be simplified to:

\[ 3x = 90° \]

Now, solving for \( x \):

\[ x = \frac{90°}{3} \] \[ x = 30° \]

Now, substituting back to find \( m∠B \):

\[ m∠B = 2x = 2(30°) = 60° \]

Thus, the measure of ∠B is:

60°