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dimulka [17.4K]
4 years ago
7

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

Mathematics
1 answer:
weeeeeb [17]4 years ago
3 0

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.

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<em><u>Solution:</u></em>

<em><u>Given system of equations are:</u></em>

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