in a geometric diagram, <A and <B are complmentary, and they from a straight line with <C. If m<A = x, m<B = (2x), and m<C = 90, wut is the measure of <B?

Question

180

30

60

90

Answer 1

To solve for the measure of angle \( B \):

1. Since angles \( A \) and \( B \) are complementary, we have: \[ m<A + m<B = 90^\circ \] Given \( m<A = x \) and \( m<B = 2x \), we can substitute these values: \[ x + 2x = 90^\circ \] \[ 3x = 90^\circ \] \[ x = 30^\circ \]

2. Now, we can find the measure of angle \( B \): \[ m<B = 2x = 2(30^\circ) = 60^\circ \]

Thus, the measure of angle \( B \) is \( \boxed{60} \).