Question

in a geometric diagram, angles a and b are complimentary, and form a straight line with angle c, angle a is x, angle b is 2x, and angle c is 90... what is the measure of angle b

Answer 1

To solve for the measure of angle \( b \), we start by using the information given about the angles.

We know that:
- Angles \( a \) and \( b \) are complementary, which means \( a + b = 90^\circ \).
- Angle \( a \) is \( x \).
- Angle \( b \) is \( 2x \).
- Angle \( c \) on the straight line is \( 90^\circ \), and it forms a straight line with angles \( a \) and \( b \).

Since angles \( a \) and \( b \) are complementary and sum to \( 90^\circ \), we can write the equation:
\[
x + 2x = 90^\circ
\]

This simplifies to:
\[
3x = 90^\circ
\]
\[
x = \frac{90^\circ}{3} = 30^\circ
\]

Now we can find the measures of angles \( a \) and \( b \):
- Angle \( a \) (which is \( x \)) is \( 30^\circ \).
- Angle \( b \) (which is \( 2x \)) is \( 2(30^\circ) = 60^\circ \).

Therefore, the measure of angle \( b \) is:
\[
\boxed{60^\circ}
\]