Question

If the angles of a triangle are 2a, a+20, and a+24, the value of 'a' is:​

Answer 1

• Value of a is 34°.

Step-by-step explanation:

Given:-

• Angles of triangle are 2a, a+20 and a+24.

To find:-

• Value of a.

Solution:-

We know,

Sum of all interior angles of triangle is equal to 180°.

So,

$\longrightarrow$ 2a + a + 20 + a + 24 = 180°

$\longrightarrow$ 4a + 20 + 24 = 180°

$\longrightarrow$ 4a + 44 = 180°

$\longrightarrow$ 4a = 180° - 44

$\longrightarrow$ 4a = 136°

$\longrightarrow$ a = 136°/4

$\longrightarrow \purple{\boxed{\sf \bold{a = 34\degree}}\star}$

Verification:-

$\longrightarrow$ 2a + a + 20 + a + 24 = 180°

• Put x = 34°

$\longrightarrow$ 2×34° + 34° + 20 + 34° + 24° = 180°

$\longrightarrow$ 68° + 54° + 58° = 180°

$\longrightarrow$ 180° = 180°

$\boxed{\sf Hence \: Verified.}$

Angles :-

2a = 2×34° = 68°

a + 20 = 34° + 20 = 54°

a + 24 = 34° + 24° = 58°

Therefore,

Value of a is 34°.

Answer 2

question:

If the angles of a triangle are 2a, a+20, and a+24, the value of 'a' is:

solution:

$\red{\sf value \: of \: a = 34°}$

Given:

three angles of triangle:

• 2a
• a+20
• a+24

To find:

The value of a?

step by step explanation:

$\boxed{ \sf sum \: of \: angles \: of \: a \: triangle = 180 \degree}$

2a + a + 20 + a + 24 = 180°

4a + 20 + 24 = 180°

4a + 44 = 180°

4a = 180° - 44°

4a = 136°

$\sf{a = \frac{136}{4} }$

a = 34°

Verification:

2a + a + 20 + a + 24 = 180°

2° × 34° + 34° + 20° + 34° + 24° = 180° ( as a = 34° )

68° + 54° + 58° = 180°

180° = 180°

hence , verified ✓

Therefore:

Three angles = 68° , 54° , 58° and A = 34°