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\\( \angle 1 \\) and \\( \angle 2 \\) are supplementary angles. if \\( m \angle 1 = ( 2 x + 16 ) ^ { \circ } \\) and \\( m \angle 2 = ( 6 x - 20 ) ^ { \circ } \\), then
find the measure of \\( \angle 1 \\).

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute the given expressions: \((2x + 16)+(6x - 20)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+6x + 16-20=180\), which gives \(8x-4 = 180\).

Step3: Solve for \(x\)

Add \(4\) to both sides: \(8x-4 + 4=180 + 4\), so \(8x=184\).
Divide both sides by \(8\): \(x=\frac{184}{8}=23\).

Step4: Find the measure of \(\angle1\)

Substitute \(x = 23\) into the expression for \(m\angle1\): \(m\angle1=(2x + 16)^{\circ}\).
\(m\angle1=(2\times23 + 16)^{\circ}=(46+16)^{\circ}=62^{\circ}\).

Answer:

\(62^{\circ}\)