Question

in the picture, line a is parallel to line b. m∠5 is 20 less than 3 times m∠8. ∠5 =
∠8 =

Explanation:

Step1: Identify angle - relationship

Since line $a$ is parallel to line $b$, $\angle5$ and $\angle8$ are supplementary angles, so $m\angle5 + m\angle8=180^{\circ}$. Let $m\angle8 = x$, then $m\angle5=3x - 20$.

Step2: Substitute into the equation

Substitute the expressions for $m\angle5$ and $m\angle8$ into the supplementary - angle equation: $(3x - 20)+x = 180$.

Step3: Simplify the equation

Combine like terms: $4x-20 = 180$.

Step4: Solve for $x$

Add 20 to both sides: $4x=180 + 20=200$. Then divide both sides by 4: $x=\frac{200}{4}=50$.

Step5: Find $m\angle5$ and $m\angle8$

Since $x = m\angle8$, then $m\angle8 = 50^{\circ}$. And $m\angle5=3x - 20=3\times50 - 20=150 - 20 = 130^{\circ}$.

Answer:

$\angle5 = 130^{\circ}$
$\angle8 = 50^{\circ}$