Question

$\angle 1$ and $\angle 2$ are supplementary angles. if $m\angle 1 = (6x - 26)\degree$ and $m\angle 2 = (6x - 10)\degree$, 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 \(m\angle1=(6x - 26)^\circ\) and \(m\angle2=(6x - 10)^\circ\) into the equation: \((6x - 26)+(6x - 10)=180\).

Step2: Solve for \(x\)

Combine like terms: \(6x+6x-26 - 10 = 180\) → \(12x-36 = 180\).
Add 36 to both sides: \(12x=180 + 36\) → \(12x=216\).
Divide by 12: \(x=\frac{216}{12}=18\).

Step3: Find \(m\angle1\)

Substitute \(x = 18\) into \(m\angle1=(6x - 26)^\circ\): \(6(18)-26=108 - 26 = 82\).

Answer:

The measure of \(\angle1\) is \(82^\circ\).