Question

Please help for 50 points with solution

Answer 1

a = 60

Explanation:

→ Find the sum of all the angles

2a + 30 + 90 - a = 180

→ Collect the a terms

a + 120 = 180

→ Find a

a = 60

Answer 2

(d) 60°

Explanation:

Theorems

• Interior angles of a triangle sum to 180°
• Angles on a straight line sum to 180°

Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

⇒ (a + 20) + (a + 10) = (a + 90)

⇒ a + 20 + a + 10 = a + 90

⇒ 2a + 30 = a + 90

⇒ 2a + 30 - a = a + 90 - a

⇒ a + 30 = 90

⇒ a + 30 - 30 = 90 - 30

⇒ a = 60