Question

(a) One of the exterior angles of a triangle is 125º and the interior opposite angles are in the ratio 2:3. Find the angles of the triangle?

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Answer 1

Step-by-step explanation:

let the interior opposite angles be 2x and 3x

2x + 3x = 125⁰ (sum of interior opposite angles is equal to opposite angle )

5x = 125⁰

x = 25⁰

angle = 50⁰ , 75⁰

now , sum of the angles of a triangle is 180⁰

180⁰-(50⁰+75⁰)

=180⁰ - 125⁰

= 55⁰

angle = 50⁰ , 75⁰ , 55⁰

Answer 2

Answer:

let the triangle be ∆abc

the the ratio be 2x and 3x

2x+3x=125° (sum of two interior angle =sum of exterior angle)

5x=125°

x=25

2x=25×2=50

3x=25×3=75

for the third angle

125-180=55