Question

⑥ a =
⑦ 2x 120° x =
⑧ a = b = c = d = e = f =
⑨ a = b = c =
⑩ 7x - 24 5x + 14 x =

Explanation:

Step1: Solve for problem 6

The sum of angles on a straight - line is 180°. So, \(a + 90^{\circ}+20^{\circ}=180^{\circ}\).

$$a=180^{\circ}-(90^{\circ} + 20^{\circ})=70^{\circ}$$

Step2: Solve for problem 7

The two angles \(2x\) and \(120^{\circ}\) are supplementary (sum to 180°). So, \(2x+120^{\circ}=180^{\circ}\).

$$2x=180^{\circ}-120^{\circ}=60^{\circ}$$

$$x = 30^{\circ}$$

Step3: Solve for problem 8

• \(a = 60^{\circ}\) (vertical angles are equal).
• \(c=a = 60^{\circ}\) (vertical angles).
• \(b = 180^{\circ}-a=120^{\circ}\) (linear - pair).
• \(d = 180^{\circ}-130^{\circ}=50^{\circ}\) (linear - pair).
• \(e = 130^{\circ}\) (vertical angles).
• \(f=d = 50^{\circ}\) (vertical angles).

Step4: Solve for problem 9

• \(x = 180^{\circ}-115^{\circ}=65^{\circ}\) (linear - pair).
• \(a=x = 65^{\circ}\) (vertical angles).
• \(c=a = 65^{\circ}\) (vertical angles).
• \(b = 180^{\circ}-a=115^{\circ}\) (linear - pair).

Step5: Solve for problem 10

The two angles \(7x - 24\) and \(5x+14\) are vertical angles, so \(7x-24=5x + 14\).

$$7x-5x=14 + 24$$

$$2x=38$$

$$x = 19$$

Answer:

1. \(a = 70^{\circ}\)
2. \(x = 30^{\circ}\)
3. \(a = 60^{\circ},b = 120^{\circ},c = 60^{\circ},d = 50^{\circ},e = 130^{\circ},f = 50^{\circ}\)
4. \(a = 65^{\circ},b = 115^{\circ},c = 65^{\circ}\)
5. \(x = 19\)