Question

one of the angle of a triangle is 120 and the other two angles are equal find the measure of the equal angle​

Answer 1

Question:One of the angle of triangle is 120°and the other two angles are equal.Find the measure of the equal angle?

Answer:

30° each

Given:

A triangle ABC in which one angle of triangle is120° and other two angles are equal

To find:

Measure of the equal angles

Solution:-

Let the other two angles be x {as both are equal}

Then

120°+x+x=180°

120°+2x=180°

2x=180-120

2x=60

x=30°

_______________

The measure of the equal angles=30°

_________________________

☆Verification☆

120°+30°+30°=180°{sum of a triangle}

180°=180°

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:}}}}$

The angles of the triangle are 120°, 30° and 30°.

$\mathfrak{\large{\underline{\underline{Step-by-step-explanation}}}}$

Given -

One Angle = 120°

The Measure of other 2 angles is same

To find -

The Measure of the Remaining angles

Solution -

Let the remaining two angles be as y, as the measure of the angles is same.

According to the Angle sum Property of Triangle ;

Sum of all angles in a triangle is 180°

$\tt{\implies} \: {120}^{\circ} + {y}^{\circ} + {y}^{\circ} = {180}^{\circ} \\ \tt{\implies} \: {120}^{\circ} + {2y}^{\circ} = {180}^{\circ} \\ \tt{\implies} \: {2y}^{\circ} = {180}^{\circ} - {120}^{\circ} \\ \tt{\implies} \:{2y}^{\circ} = {60}^{\circ} \\ \tt{\implies} \:{y}^{\circ} = \frac{60}{2}\\ \tt{\implies} \:{y}^{\circ} = {30}^{\circ}$

As y = 30°, both the angles are 30°

$\therefore$ The angles of the triangle are 120°, 30° and 30°.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Check if the sum of the angles is 180° or not.

$\tt{\implies} \:{120}^{\circ} + {30}^{\circ} + {30}^{\circ} = {180}^{\circ} \\ \tt{\implies} \: {120}^{\circ} + {60}^{\circ} = {180}^{\circ} \\ \tt{\implies} \: {180}^{\circ} = {180}^{\circ}$

LHS = RHS

$\therefore$ The angles of the triangle are 120°, 30° and 30°.