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

`\angle 4=160^(\circ), \angle 6=20^(\circ)`

Explanation:

Consider the below figure attached with this question.

Given information: a∥b,
`\angle 6=(1)/(8)\angle 4`.

a∥b (Given)

`\angle 6=(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.