Question

one side of triangle is produced and the exterior opposite angle be in ratio 3:5 find the measures of each angle of triangle.
please answer me first
​

Answer 1

Answer:

have the property that, in a triangle exterior angle is equal to the sum of interior opposite angles.

Given, the interior opposite angles to the exterior angle 105

∘

are in the ration 2:5

∴2x+5x=105

o

7x=105

o

⟹x=15

o

Therefore the interior opposite angles to the angle 105

o

are 2x=2(15)=30

o

and 5x=5(15)=75

o

Let the third angle of the triangle be C

We have the sum of interior angles of a triangle is 180

o

∴30

o

+75

o

+C=180

o

C=180

o

−75

o

−30

o

=180

o

−105

o

C=75

o

Hence, the angles are 30

o

,75

o

,75

o

.