Question

one side of a triangle is produced , the exterior angle so formed is 140° . if the corresponding interior opposite angles are in the ratio 3:4, find the measure of all the angles of the triangle​

Answer 1

✪ Question ✪

One side of a triangle is produced, the exterior angle so formed is 140°. If the corresponding interior opposite angles are in the ratio 3:4, find the measure of all the angles of the triangle.

✪ Given ✪

Exterior angle = 140°

Ratio of opposite angles = 3:4

✪ To find ✪

The measure of all angles.

✪ Solution ✪

Let the opposite angles are 3x° and 4x°.

Since the sum of opposite two angles is equal to the exterior angle, we can say-

$3x+4x = 140$

⇒ $7x = 140$

⇒ $x=\frac{140}{7}$

⇒ $x=20$

✪ Hence ✪

x = 20

3x° = (3×20)° = 60°

4x° = (4×20)° = 80°

Let the 3rd angle be y°.

As we know that the sum of all angles of a triangle is 180°, we can say-

$y+60+80=180$

⇒ $y+140=180$

⇒ $y=180-140$

⇒ $y = 40$

So, 3rd angle = y° = 40°

✪ Therefore ✪

All the angles of the triangle are 60°, 80° and 40°.

๑ Hope this helps you. ๑