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.

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11-01-2020
Mathematics

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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.

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rani01654 rani01654 · Answer 1 · 2020-01-18T13:11:25+01:00

Answer:

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)

psm22415 psm22415 · Answer 2 · 2021-12-22T19:17:38+01:00

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.

The sum of the measure of two angles is 180 degrees, then the pair of angles is said to be supplementary angles. 110° and ∠ 1 are supplementary.

Then, ∠1 = 180° - 110° = 70° .

Corresponding angles are formed when two lines are crossed by another line (which is known as Transversal).

Then, ∠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.

Then, ∠3 = ∠2 = 180° - 115° = 65°

The ∠1, ∠2, and ∠7 form 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°

When two lines intersect they form four angles. Vertical angles are the angles that are opposite to each other.

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°

To know more about Triangles click the link given below.

https://brainly.com/question/23044118