Parallel lines q and m are cut by transversal lines j and k. the lines, and the measures of some of the angles created by the intersections of the lines, are shown in the diagram below.

The measure of angle ∠1 is 70°.

The measure of angle ∠3 is 65°.

The measure of angle ∠5 is 45°.

The measure of angle ∠6 is 45°.

Given that,

Parallel lines q and m are cut by transversal lines j and k.

The lines, and the measures of some of the angles created by the intersections of the lines, are shown in the diagram below.

We have to determine,

What is the measure in the degree of ∠1, ∠3, ∠5, and ∠6?

According to the question.

        Then, ∠1 = 180° - 110° = 70° .

       Then, ∠2 and ∠3 are corresponding angles, so they are equal.

         Now, 115° and ∠2 are supplementary angles.

        So, 115° and ∠3 are also supplementary.

        Then, ∠3 = ∠2 = 180° - 115° = 65°

         Hence, ∠ 1 + ∠ 2 + ∠7 = 180°

        = 70° + 65° + ∠7 = 180°

         = ∠7 = 45°

        Now, ∠7 and ∠5 are equal as they are corresponding angles.

        Since line q and line m are parallel and line j is transverse.

        So, ∠5 = 45°

Any two intersecting lines form two pairs of vertical angles that are opposite to each other.

Then, ∠7 = ∠6 {Vertically opposite angles}

So, ∠6 = 45°

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a. ∠ 1 = 70°

b. ∠ 3 = 65°

c. ∠ 5 = 45°

d. ∠ 6 = 45°.

Step-by-step explanation:

See the attached diagram.

a. 110° and ∠ 1 are supplementary.

Hence, ∠ 1 = 180° - 110° = 70° (Answer)

b. Now, ∠ 2 and ∠ 3 are corresponding angles, so they are equal.

Since line q and m are parallel and line k is transverse.

Now, 115° and  ∠ 2 are supplementary angles.

So, 115° and ∠ 3 are also supplementary.

Hence, ∠ 3 = ∠ 2 = 180° - 115° = 65° (Answer)

c. Now, ∠ 1, ∠ 2, and ∠ 7 forms a triangle.

Hence, ∠ 1 + ∠ 2 + ∠ 7 = 180°

⇒ 70° + 65° + ∠ 7 = 180°

⇒ ∠ 7 = 45°

Now, ∠ 7 and ∠ 5 are equal as they are corresponding angles.

Since, line q and line m are parallel and line j is transverse.

So, ∠ 5 = 45° (Answer)

d. Now, ∠ 7 = ∠ 6 {Vertically opposite angles}

So, ∠ 6 = 45° (Answer)

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step-by-step explanation: