Question

One of the exterior angles of a triangle is 120 and it's interior opposite angles are equale to each other .What is the measure of each of these two angles​

Answer 1

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Given

• Exterior Angle,A = 120°

• Both the interior angles are equal to eachother

Let the interior angles be "B" and "C" » B = C

NOTE

The exterior angle of a triangle is equal to the sum of the interior angles opposite to it

Since,both the angles are opposite to the exterior angle.

A = 2(B + C)

But B = C,

→ 120° = 2B

→ 120° = 2B

→ B = 60°

and C = 60°

Thus,the required angle is 60°

Answer 2

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Measure of the interior opposite angles is 60°

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GiVeN :

• One of the exterior angles of a triangle is 120°
• The Interior opposite angles of triangle are equal to each other.

To FiNd :

• The measure of each of these two angle (Interior opposite angles)

SoLuTiOn :

Let the measure of the one of the interior opposite angles be x.

Let the measure of the other interior opposite angle be y.

Since, the two interior opposite angles are equal, we can say that,

• x = y ---> (1)

Exterior angle = 120°

Property of exterior angle of triangle :

• An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Which means,

• 120° = x° + y°

$\longrightarrow$ $\sf{x\:+\:y\:=\:120}$

$\longrightarrow$ $\sf{x\:+\:x\:=\:120}$

$\sf{\because{x\:=\:y\:from\:eq.1}}$

$\longrightarrow$ $\sf{2x\:=\:120}$

$\longrightarrow$ $\sf{x\:=\:{\dfrac{120}{2}}}$

$\longrightarrow$ $\sf{x\:=\:60}$

From equation 1,

$\longrightarrow$x = y

$\longrightarrow$ y = 60°

•°• Measure of the interior opposite angle is 60°