Question

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.

Answer 1

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)