Question

If m∠1 = 2x + 20 and m∠6 = 3x + 30

Find:
1.) the value of x with solution =
2.) m∠1 =
3.) m∠2 =
4.) m∠3 =
5.) m∠4 =
6.) m∠5 =
7.) m∠6 =
8.) m∠7 =
9.) m∠8 = ​​

Answer 1

1) x = 26°

2) 82°

3) 82°

4) 108°

5) 108°

6) 108°

7) 108°

8) 82°

9) 82°

Explanation:

Given:

∠1 = 2x + 20

∠6 = 3x + 30

1) ∠1 + ∠6 = 180 (adjacent angles)

2x + 20 + 3x + 30 = 180°

5x + 50 = 180°

5x = 180 - 50°

5x = 130°

x = 26°

2) ∠1 = 2 × 26 + 30 = 52 + 30 = 82°

3) ∠2 = ∠1 = 82° (cross angles)

4) ∠3 = ∠6 = 3x + 30

∠3 = 3 × 26 + 30 = 78 + 30 = 108°

5) ∠4 = ∠6 = 108° (cross angles)

6) ∠5 = ∠3 = 108° (cross angles)

7) ∠6 = 108°

8) ∠7 = ∠1 = 82° (cross angles)

9) ∠8 = ∠2 = 82° (cross angles)