Question

$\angle1$ and $\angle2$ are supplementary angles. if $m\angle1=(4x - 28)^{circ}$ and $m\angle2=(7x - 12)^{circ}$, then find the measure of $\angle1$.

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(4x - 28)^{\circ}\) and \(m\angle2=(7x - 12)^{\circ}\) into the equation: \((4x - 28)+(7x - 12)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(4x+7x-28 - 12 = 180\), which gives \(11x-40 = 180\).

Step3: Solve for \(x\)

Add 40 to both sides of the equation: \(11x-40 + 40=180 + 40\), so \(11x=220\).
Divide both sides by 11: \(x=\frac{220}{11}=20\).

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

Substitute \(x = 20\) into the expression for \(m\angle1\): \(m\angle1=(4x - 28)^{\circ}=(4\times20 - 28)^{\circ}\).
First, calculate \(4\times20=80\), then \(80-28 = 52^{\circ}\).

Answer:

\(52^{\circ}\)