Question

one side of a triangle is produced and the exterior angle so formed is 128 degrees if the interior opposite angles are equal find the measures of the angles of a triangle
if you will say the correct answer I will mark you as the brainlist.​

Answer 1

Answer :-

Given :-

• Exterior angle = 128°
• Interior opposite angle are equal

To Find :-

• Measure of the angles of the traingle

Solution :-

We know that,

Exterior angle is equal to the sum of interior opposite angle.

Let interior opposite angles be x

→ x + x = 128

→ 2x = 128

→ x = 128 / 2

→ x = 64

Interior opposite angles = 64°

Let the third angle be y

Applying angle sum property in triangle :-

→ x + x + y = 180°

→ 64 + 64 + y = 180°

→ y + 128 = 180°

→ y = 52°

Angles of triangle = 52° , 64° and 64°

Answer 2

Given :-

$~~~~~~~$

• Exterior angle = 128°
• Interior opposite angle are equal

$~~~~~~~~$

To find :-

$~~~~~~~~$

• Measure of the angles of the triangle.

$~~~~~~~$

Solution :-

$~~~~~~$

★ We know that,

• Exterior angle is equal to the sum of interior opposite angle.

$~~~~~~~$

Let interior opposite angles be x

$~~~~~~~~$

$\rightarrow$ $\large{\tt{x + x = 128}}$

$~~~~~~~~$

$~~~~~$$\rightarrow$ $\large{\tt{2x = 128}}$

$~~~~~~~~$

$~~~~~~~~$$\rightarrow$ $\large{\tt{x = \frac{128}{2}}}$

$~~~~~~~~$

$~~~~~~~~~~~~~$$\rightarrow$ $\large{\tt{x = \dfrac{\cancel{128}}{\cancel{2}}}}$

$~~~~~~~~$

$~~~~~~~~~~~~~~~~$$\rightarrow$ ${\underline{\boxed{\purple{\bf{x = 64}}}}}$★

$~~~~~~~$

Interior opposite angles = 64°

$~~~~~~$

$~~~~~~~~~~~$ $\large\dag$ Let the third angle be y :

$~~~~~~~~$

Applying angle sum property in triangle :

$~~~~~~$

$\rightarrow$ $\large{\tt{x + x + y = 180°}}$

$~~~~~~$

$~~~~~$$\rightarrow$ $\large{\tt{64 + 64 + y = 180°}}$

$~~~~~~$

$~~~~~~~~~$$\rightarrow$ $\large{\tt{y + 128 = 180°}}$

$~~~~~~~$

$~~~~~~~~~~~~~$$\rightarrow$ ${\underline{\boxed{\purple{\bf{y = 52°}}}}}$★

$~~~~~~~$

$\large\dag$ Hence Proved

$~~~~~$

• Angles of triangle = 52° , 64° and 64°