Question

$\angle 1$ and $\angle 2$ are supplementary angles. if $m\angle 1 = (3x - 23)\degree$ and $m\angle 2 = (7x - 17)\degree$, then find the measure of $\angle 1$.

Explanation:

Step1: Recall supplementary angles property

Supplementary angles add up to \(180^\circ\). So, \(m\angle1 + m\angle2 = 180^\circ\).
Substitute \(m\angle1=(3x - 23)^\circ\) and \(m\angle2=(7x - 17)^\circ\) into the equation:
\((3x - 23)+(7x - 17)=180\)

Step2: Simplify and solve for x

Combine like terms:
\(3x+7x-23 - 17=180\)
\(10x-40 = 180\)
Add 40 to both sides:
\(10x=180 + 40\)
\(10x=220\)
Divide both sides by 10:
\(x = 22\)

Step3: Find \(m\angle1\)

Substitute \(x = 22\) into \(m\angle1=(3x - 23)^\circ\):
\(m\angle1=3(22)-23\)
\(m\angle1 = 66-23\)
\(m\angle1 = 43^\circ\)

Answer:

\(43^\circ\)