Question

∠1 and ∠2 are supplementary angles. if ( mangle1 = (7x + 16)^circ ) and ( mangle2 = (3x + 24)^circ ), then find the measure of ( angle1 ).

Explanation:

Step1: Recall supplementary angles sum to \(180^\circ\)

Since \(\angle1\) and \(\angle2\) are supplementary, \(m\angle1 + m\angle2 = 180^\circ\). Substitute \(m\angle1=(7x + 16)^\circ\) and \(m\angle2=(3x + 24)^\circ\):
\((7x + 16)+(3x + 24)=180\)

Step2: Solve for \(x\)

Combine like terms: \(10x + 40 = 180\).
Subtract 40 from both sides: \(10x = 140\).
Divide by 10: \(x = 14\).

Step3: Find \(m\angle1\)

Substitute \(x = 14\) into \(m\angle1=(7x + 16)^\circ\):
\(m\angle1 = 7(14)+16 = 98 + 16 = 114\).

Answer:

\(114\)