Solve Equations with Complementary Angles Quick Check

Question

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Question
A figure displays two nonadjacent angles with measures 3x°
and (4x+1)°
. If the angles are complementary, what is the simplified equation corresponding to the measures of the angles?(1 point)
Responses

(7x+1)°=90°
left parenthesis 7 x plus 1 right parenthesis degrees equals 90 degrees

(7x+1)°=180°
left parenthesis 7 x plus 1 right parenthesis degrees equals 180 degrees

(1x+1)°=180°
left parenthesis 1 x plus 1 right parenthesis degrees equals 180 degrees

(1x+1)°=90°
left parenthesis 1 x plus 1 right parenthesis degrees equals 90 degrees
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Answer 1

To determine the correct equation for the two angles given that they are complementary, we start by recalling that complementary angles add up to 90 degrees.

The angles provided are \( 3x^\circ \) and \( (4x + 1)^\circ \).

So, the equation can be set up as follows:

\[ 3x + (4x + 1) = 90 \]

Now, simplify the left side:

\[ 3x + 4x + 1 = 90 \]

This combines to:

\[ 7x + 1 = 90 \]

This leads us to the simplified equation:

\[ (7x + 1)^\circ = 90^\circ \]

Thus, the correct response is:

(7x + 1)° = 90°.