Question

$\angle 1$ and $\angle 2$ are supplementary angles. if $m\angle 1 = (x - 30)\degree$ and $m\angle 2 = (x - 26)\degree$, then find the measure of $\angle 1$.

Explanation:

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\). So, \(m\angle1 + m\angle2 = 180^\circ\).
Substitute \(m\angle1=(x - 30)^\circ\) and \(m\angle2=(x - 26)^\circ\) into the equation: \((x - 30)+(x - 26)=180\).

Step2: Solve for \(x\)

Simplify the left - hand side: \(x-30+x - 26 = 180\)
Combine like terms: \(2x-56 = 180\)
Add 56 to both sides: \(2x=180 + 56\)
\(2x=236\)
Divide both sides by 2: \(x=\frac{236}{2}=118\)

Step3: Find \(m\angle1\)

Substitute \(x = 118\) into \(m\angle1=(x - 30)^\circ\): \(m\angle1=(118 - 30)^\circ=88^\circ\)

Answer:

\(88^\circ\)