Question

One of the exterior angle of a triangle is 100° and its opposite angles are in a ratio of 1:4

Answer 1

Answer:

20°, 80° and 80°

Step-by-step explanation:

Exterior angle = ∠ACD = 100°

∠BAC : ∠ABC = 1 : 4

Let ∠BAC = x and ∠ABC = 4x

An exterior angle of a triangle is equal to the sum of the  interior opposite angles.

⇒ x + 4x = 100

⇒ 5x = 100

⇒ x = 100/5

⇒ x = 20°

∴∠BAC = x  = 20°

and ∠ABC = 4x = 4 * 20 = 80°

Sum of all interior angles of a trriangle is 180°

∠BAC + ∠ABC + ∠BCA = 180°

⇒ 20° + 80° + ∠BCA = 180°

⇒ 100° +  ∠BCA = 180°

⇒  ∠BCA = 180° - 100°

⇒  ∠BCA = 80°

So, the angles of the triangle are 20°, 80° and 80°