Question

the angle of a triangle are (2x-8)° (6x-4)° (4x)°.find the value of x,and the measure of each angle​

Answer 1

Answer :

›»› The measure of each angle of a triangle is 24°, 92°, and 64°.

Given :

• The angle of a triangle are (2x - 8)°, (6x - 4)°, (4x)°.

To Find :

• The value of x = ?
• The measure of each angle of a triangle = ?

Solution :

As we know that

The sum of all three angles of a traingle is 180°. This statement is called angle sum property of a traingle.

→ (2x - 8) + (6x - 4) + (4x) = 180

→ 2x - 8 + 6x - 4 + 4x = 180

→ 2x + 6x + 8x - 8 - 4 = 180

→ (2 + 6 + 8)x - 8 - 4 = 180

→ 12x - 8 - 4 = 180

→ 12x - 12 = 180

→ 12x = 180 + 12

→ 12x = 192

→ x = 192 ÷ 12

→ x = 16

Hence, the value of x is 16.

Therefore,

The measure of each angle of a triangle will be,

→ 2x - 8

→ 2 × 16 - 8

→ 32 - 8

→ 24°.

→ 6x - 4

→ 6 × 16 - 4

→ 96 - 4

→ 92°.

→ 4x

→ 4 × 16

→ 64°.

Hence, the measure of each angle of a triangle is 24°, 92°, and 64°.

Verification :

The sum of all three angles of a triangle is 180°.

→ 24 + 92 + 64 = 180

→ 116 + 64 = 180

→ 180 = 180

Here, LHS = RHS

Hence Verified !

Answer 2

Answer:

$\huge \bf \: required \: answr$

As we know that sum of all sides of triangle is 180⁰.

Now,

$\sf \implies \: (2x - 8) \: \: (6x - 4) \: \: (4x)$

$\sf \implies \: 2x - 8 \: + \: 6x - 4 \: + \: 4x= 180⁰$

$2x + 6x + 4x = 8 - 4= 180⁰$

$(2 + 6 + 4)x - 8 - 4 = 180$

$12x - 8 - 4 = 180$

$12x - 12 = 180$

$12x = 180 + 12$

$12x = 192$

$x = \frac{192}{12}$

$x = 16$

Now,

First angle = 2 × 16 - 8

First angle = 32-8

First angle = 24

Second angle = 6 × 16 - 4

Second angle = 96-4

Second angle = 92

Third angle = 4 × 16

Third angle = 64

Verification

$24 + 92 + 64 = 180$

$180 = 180$

LHS = RHS