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Fill out the question marks

Fill out the question marks-example-1
User He
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Let's analyze the given information:

1. LCDE and LEDF are supplementary: \( m\angle CDE + m\angle LEDF = 180^\circ \).

2. Angles that form a linear pair are supplementary: \( x + (3x + 20) = 180^\circ \).

Now, let's solve for x:

a. Combine like terms: \( x + 3x + 20 = 180 \).

b. Combine the x terms: \( 4x + 20 = 180 \).

c. Subtract 20 from both sides: \( 4x = 160 \).

d. Divide by 4: \( x = 40 \).

So, the value of x is 40. Now, substitute this value back into the expression for angle \( (3x + 20) \):

\[ (3 \times 40 + 20)^\circ = 120 + 20 = 140^\circ \].

Therefore, the measure of angle \( (3x + 20) \) is \( 140^\circ \), and the correct answer is option (e).
User Chris Fellows
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