Question

An exterior angle of a triangle is 105 degree and one of the interior opposite angles is double the other then find the all interior angles of the triangle​

Answer 1

Answer:

35°, 70° and 75° are the three interior angles of the triangle.

Step-by-step explanation:

Given,

• Measure exterior angle = 105°

To find :

• the all interiors angles.

Let x and 2x be the two interior opposite angles.

Now,

x + 2x = 105°

⇒3x = 105°

⇒x = 105°/3

⇒x = 35°

.°. x = 35°

Then, the interior opposites angles are x = 35° and 2x = 35° × 2 = 70°.

Here,

Let y be the other interior angle.

35° + 70° + y = 180°

➝ 105° + y = 180°

➝ y = 180° - 105°

➝ y = 75°

Hence, the three interior angles are 35°, 70° & 75° .

Answer 2

Answer:

$\huge \sf \: required \: answer$

Exterior angle = 105⁰

Let the interior angle be x , 2x

$x + 2x = 105 \degree$

$3x = 105 \degree$

$x = 105 \div 3$

$x = 35$

Now,

first angle = 35⁰

Second angle = 35 × 2 = 70⁰

Let Third angle = y

$35 + 70 + y = 180$

$105 + y = 180$

$y = 180 - 105$

$y = 75$

$\bf \: interior \: angle \: \: = 35 \: and \: 70 \: and \: 75$

Verification

35⁰+70⁰+75⁰ = 180⁰

105⁰+75⁰=180⁰

180⁰ = 180⁰

LHS = RHS