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)
