Question

One of the exterior angle of a triangle is 100° and the interior angles are in
ratio 3:2. Find the angles of the triangle.​

Answer 1

$\huge\blue{\boxed{\underline{ANSWER}}}$

GIVEN

$➲$ Exterior angle of a triangle = 100°

$➲$ The interior angle are in ratio 3:2

TO FIND:

$➱$ The angle of triangle.

SOLUTIONS

$➵$ we know that the sum of interior angle of triangle is equal to the exterior angle of triangle.

so.

$➲$ let the interior angle of triangle are 3x and 2x .

Now:-

$➡ \: \: 3x + 2x = 100 \\ ➡ \: \: 5x = 100 \: \: \: \: \: \: \: \: \: \: \\ ➡ \: \: x = \cancel\frac{100}{5} \: \: \: \: \: \: \: \: \: \: \: \\ ➡ \: \: x = 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now the interior angle of triangle which has been given in ratio

$➱$ 3x = 3×20 = 60°

$➱$ 2x = 2 × 20 = 40°

$➾$ Now let the third angle of triangle is y

• The sum of the all angles of triangle is equal to 180°

$&#10145 \: \: 60 + 40 + y = 180 \\ &#10145 \: \: 100 + y = 180 \: \: \: \: \: \: \: \: \\ &#10145 \: \: y = 180 - 100 \: \: \: \: \: \: \: \: \\ &#10145 \: \: y = 80 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$➾$ Now the all three angles of triangle are 60°, 40°, 80°.

Answer 2

Step-by-step explanation:

the first angle will be 80 because one exterior angle is given and one interior and one exterior angle makes a linear pair so 100+80=180

as we know the sum of all the angles 180 so

3x +2x+80=180 as they are in ratios 3:2

5x+80=180

5x=180=80 = 100

x=100/5

x=20

3x=20*3=60

2x=20*2 = 40

60+40+80=180

therefore the other 2 sides are 60 and 40