Question

one side of one side of a triangle is produced and the exterior angles so formed is 125 degrees if the interior opposite angles are in ratio 2 is to 3 find the measure of all angles of the triangle​

Answer 1

Step-by-step explanation:

let the common ratio = x

then.

interior opp. angle of triangle are 2x, 3x

then

2x+3x =125

5x = 125

x =125÷5

x = 25

then 2x = 2×25 = 50°

3x = 3×25 = 75°

We know that sum interior angle is 180°

then

x+ 75°+50° = 180°

x = 180°-125

x= 55°

Answer 2

Let the interior opposite angles be A° and B° and the angle produced be C° and the exterior opposite angle be D°.

Then, C°+D°=180° [Exterior angle property]

Or, C°+125°=180°

Or,C°=180°-125°=55°

A°+B°=125°

Or, 2x+3×=125°

Or,5x=125°

Or,x=125°/5=25°

A°=25°×2=50°

B°=25°×3=75°