Question

An exterior angle of a triangle is 104 degrees and its interior opposite angles are in the ratio 3:5 the angle of a triangle

Answer 1

Answer :-

• The angle are A = 39° , B = 65° and C = 76°.

Given :-

• Ratio of interior angles = 3:5

To find :-

• The angles of the triangle.

Step by step explanation :-

Detailed explanation of solution :-

Let's understand!

In the question, Given that, Interior angles are in the ratio of 3 : 5 and an exterior angle of a triangle is 104 degrees.

We are asked to find angles of the triangle.

How to solve ?

In ∆ ABC, A = 3x , B = 5x and D = 104.

We know that, The sum of two Interior angles is equal to the exterior angle.

Now let's use this and do it!

Calculations :-

Therefore, The equation will be :-

3x + 5x = 104°

8x = 104°

x = $\sf \dfrac{104}{8}$

x = 13.

Thus, The value of x is 13°.

Therefore, The angles of the triangle is as follows :-

• 3x = 3 × 13 = 39°.
• 5x = 5 × 13 = 65°.

Hence, The angles are A = 39° , B = 65°.

Now, Let's also find interior angle C.

39 + 65 + C = 180°

104 + C = 180°

x = 76°

So, Interior angle C = 76°.

Verification :-

Let's add all the angles , And check whether we get 180° or not.

A + B + C = 180°

39° + 65° + 76° = 180°

180° = 180°

LHS = RHS.

Hence , Verified.

Answer 2

Given:-

• Ratio of interior angles = 3:5.

To Find:-

• The angles of the triangle = ?

Solution:-

In ∆ ABC,

Let A be = 3x.

Let B be = 5x.

The value of D is given here = 104°.

According to the question

$\sf \implies \: 3x + 5x = 104 \degree \\ \\ \sf \implies \: 8x = 104 \degree \\ \\ \sf \implies \: x = \frac{104}{8} \\ \\ \sf \implies \: x = 13 \degree$

Thus,The value of x is 13°.

Therefore,The angles of the triangle is

• 3x = 3 × 13 = 39°
• 5x = 5 × 13 = 65°

Hence,The angles are A = 35°,B = 65°

Now, Let's find interior angle C.

39° + 65° + C = 180°

104° + C = 180°

x = 76°

So, interior angle C = 76°