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Zathan Simmons
7th Grade
ASSESSMENT - Math 7B U3L12 Angles Apply Sample Work (CCT)
Question Id : 617550
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10 of 2010 of 20 Items
12:50

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

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°
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Answer 1

To find the appropriate equation for the problem, let's break down the information given:

1. Angle ABC and angle DEF are complementary angles. This means that the sum of their measures is 90°.
2. The measure of angle ABC is twice the measure of angle DEF.

Let’s denote:

• \( x \) as the measure of angle DEF.
• Therefore, the measure of angle ABC would be \( 2x \) (since it's twice the measure of angle DEF).

Since angle ABC and angle DEF are complementary, we can set up the following equation:

\[ x + 2x = 90° \]

This simplifies to:

\[ 3x = 90° \]

To find the measure of angle DEF, we would solve for \( x \).

Among the given options, the equation that corresponds to this is:

C. \( 2x + x = 90° \)

This correctly represents that angle ABC (which is \( 2x \)) plus angle DEF (which is \( x \)) equals 90°.

So the correct answer is C. \( 2x + x = 90° \).