Question

Help with this problem please!

Answer 1

1. To solve for x, you can see that nearby C and D, the two angles are equal. We can ,therefore, make an equation and solve it:
5x - 29 = 3x + 19
- 3x
2x - 29 = 19
+ 29
2x = 48
÷ 2
x = 24

2. So for this part you would substitute the value of x and then minus that angle from 180:
3 × 24 = 72
72 + 7 = 79°
180 - 79 = 101° = ∠1

3. 180 = 101 = 79° = ∠2

4. 180 - 79 = 101° = ∠3

5. Angle 4 is equal to angle 3 because there is an alternate angle (z angle) so 101° = ∠4

6. 180 - 101 = 79° = ∠5

7.  180 - 101 = 79° = ∠6

8. To find angle 7, you have to substitute in x again, so:
5 × 24 = 120
120 - 29 = 91
180 - 91 = 89° = ∠7

9. Angle 8 is the same as angle 7 because they are opposite angles, so 89° = ∠8

10. Angles 2 and 3 are supplementary, which means they add up to 180°.

I hope this helps! :)