Angle ABC and angle DEF are complementary angles. The measure of angle ABC is twice the measure of angle DEF.

Question

Which equation could be used to find, x, the measure of angle DEF?

Responses
A x + x = 90°x + x = 90°
B 2x + x = 180°2 x + x = 180°
C 2x + x = 90°
2 x + x = 90°
D x + x = 180°x + x = 180°

Answer 1

To solve for the measure of angle DEF (which we'll represent as \( x \)), we know that complementary angles are two angles whose measures add up to \( 90^\circ \). Given that angle ABC is twice the measure of angle DEF, we can express angle ABC in terms of \( x \):

1. Let the measure of angle DEF be \( x \).
2. Then the measure of angle ABC is \( 2x \).

Since the two angles are complementary, we can set up the equation:

\[ x + 2x = 90^\circ \]

This simplifies to:

\[ 3x = 90^\circ \]

Thus, the appropriate equation you are looking for is:

\[ x + 2x = 90^\circ \]

From the choices given, this corresponds to:

C) \( 2x + x = 90^\circ \)

So, the correct answer is C.