Question

question
\\( \angle 1 \\) and \\( \angle 2 \\) are supplementary angles. if \\( m \angle 1 = ( 7 x + 21 ) ^ { \circ } \\) and \\( m \angle 2 = ( x - 17 ) ^ { \circ } \\), then find the
measure of \\( \angle 2 \\).
answer attempt 1 out of 3
\\( \square ^ { \circ } \\)
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score: 1/5 penalty: 1 off
angle terminology with equations

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(7x + 21)^{\circ}\) and \(m\angle2=(x - 17)^{\circ}\) into the equation:
\((7x + 21)+(x - 17)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+x+21 - 17=180\), which simplifies to \(8x+4 = 180\).

Step3: Solve for \(x\)

Subtract \(4\) from both sides: \(8x=180 - 4=176\).
Divide both sides by \(8\): \(x=\frac{176}{8}=22\).

Step4: Find the measure of \(\angle2\)

Substitute \(x = 22\) into \(m\angle2=(x - 17)^{\circ}\):
\(m\angle2=(22-17)^{\circ}=5^{\circ}\)

Answer:

\(5\)