Question

Given that measure of angle 6 is 1/8 of measure of angle 4. Find the measures of these two angles if a∥b .

Answer 1

Answer:

$\angle 4=160^{\circ}, \angle 6=20^{\circ}$

Step-by-step explanation:

Consider the below figure attached with this question.

Given information: a∥b, $\angle 6=\frac{1}{8}\angle 4$.

a∥b              (Given)

$\angle 6=\frac{1}{8}\angle 4$    (Given)

Multiply both sides by 8.

$8\angle 6=\angle 4$      ...(1)

If a transversal line intersect two parallel lines then the same sided interior angles and are supplementary angles.

$\angle 6+\angle 4=180$              (Same sided interior angles)

$\angle 6+8\angle 6=180$            (Substitution)

$9\angle 6=180$

Divide both sides by 9.

$\angle 6=20$

The measure of angle 6 is 20 degree.

Substitute this value in equation (1).

$8(20)=\angle 4$

$160=\angle 4$

The measure of angle 4 is 160 degree.