Question

The measure of an external angle ofa trangle is 80 and the ratio of the two intemal opposite
angles is 3:5 What is the measure of its adjacent intemal angle ?​

Answer 1

$answer$

3 :5

one of the exterior angles of a triangle is 80 degrees and the interior opposite angles are in the ratio 3 :5

.

Exterior angle = sum of interior opposite angles

let the interior angles be 3x and 5x

80=3x+5x

80=8x

x= 10

the angles are 30,50

the other angle is 180-(30+50) = 100

Answer 2

Answer:

100°

Step-by-step explanation:

The measure of an external angle ofa trangle is 80 and the ratio of the two intemal opposite

angles is 3:5

Let assume ABC is Triangle and angle ACD is external angle

So Angle ACD= 80°

and angle ABC : angle BAC = 3:5

angle ABC = 3x and angle BAC = 5x

angle ABC + angle BAC = angle ACD

3x + 5x = 80

8x = 80

x = 80/8

x= 10

angle ABC = 3x = 3×10 = 30°

angle BAC = 5x = 5×10 = 50°

Now, in Triangle ABC,

Angle A + Angle B + Angle C = 180°

30° + 50° +Angle C = 180°

80° + Angle C = 180°

Angle C = 180°- 80°

Angle C = 100°