Question

∠1 and ∠2 are supplementary angles. if (mangle1=(3x + 15)^{circ}) and (mangle2=(5x - 11)^{circ}), then find the measure of ∠1.

Explanation:

Step1: Use supplementary - angle property

Since $\angle1$ and $\angle2$ are supplementary angles, $m\angle1 + m\angle2=180^{\circ}$. So, $(3x + 15)+(5x - 11)=180$.

Step2: Simplify the left - hand side

Combine like terms: $3x+5x+15 - 11=180$, which gives $8x + 4=180$.

Step3: Solve for $x$

Subtract 4 from both sides: $8x=180 - 4=176$. Then divide both sides by 8: $x=\frac{176}{8}=22$.

Step4: Find the measure of $\angle1$

Substitute $x = 22$ into the expression for $m\angle1$: $m\angle1=(3x + 15)^{\circ}=(3\times22 + 15)^{\circ}=(66+15)^{\circ}=81^{\circ}$.

Answer:

$81$