Question

The two interior opposite angles of an exterior angle of a triangle LMN are 600 and 800

.Find the

measure of the exterior angle.​

Answer 1

Answer:

140°

Step-by-step explanation:

According to the exterior angle property, the sum of two interior opposite angles is equal to the exterior angle.

Given, two interior angles = 60° and 80°.

Measure of the exterior angle = 60° + 80° = 140°

Answer 2

➤ Correct Question :-

The two interior opposite angles of an exterior angle of a triangle LMN are 60° and 80°. Find the measure of the exterior angle.

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★ How to do :-

Here, we are given with a triangle in which we are also given with two of the angles which are in the interior of the triangle. Those two angles will be the opposite interior angles of the triangle. We are asked to find the value of the exterior angle of that triangle. We have two methods to find the value of the exterior angle when two of it's interior opposite angles' measurements are provided to us. We can solve both the methods in this question. The first method is the most easier and we have only one formula in that method, whereas in the second method, we have two different formulas to find the value of the exterior angle of the triangle. As we know that always, all the triangle's angles together measure up to 180°. This is the basic concept. We can use this concept also to find out the answer. So, let's!!

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➤ Solution :-

Method ${\bf 1}$ :-

${\sf \longrightarrow \underline{\boxed{\sf E = Sum \: of \: interior \: opposite \: angles}}}$

Substitute the given values.

${\sf \leadsto E = {60}^{\circ} + {80}^{\circ}}$

Add the values to get the answer.

${\sf \leadsto E = {140}^{\circ}}$

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Method ${\bf 2}$ :-

${\sf \longrightarrow \underline{\boxed{\sf {Sum \: of \: all \: angles}_{(Triangle)}= {180}^{\circ}}}}$

Write the angles' name.

${\sf \leadsto \angle{L} + \angle{M} + \angle{N} = {180}^{\circ}}$

Substitute the given values.

${\sf \leadsto {60}^{\circ} + {80}^{\circ} + \angle{N} = {180}^{\circ}}$

Remove the degree symbol which makes easier to solve.

${\sf \leadsto 60 + 80 + \angle{N} = 180}$

Add the numbers on LHS.

${\sf \leadsto 140 + \angle{N} = 180}$

Shift the number 140 from LHS to RHS, changing it's sign.

${\sf \leadsto \angle{N} = 180 - 140}$

Substract the values.

${\sf \leadsto \angle{N} = {40}^{\circ}}$

Now, let's find the exterior angle.

${\sf \longrightarrow \underline{\boxed{\sf Straight \: line \: angle = {180}^{\circ}}}}$

Substitute the given values.

${\sf \leadsto {40}^{\circ} + x = {180}^{\circ}}$

Shift the number 40 from LHS to RHS, changing it's sign.

${\sf \leadsto x = {180}^{\circ} + {40}^{\circ}}$

Subtract the values.

${\sf \leadsto x = {140}^{\circ}}$

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${\red{\underline{\boxed{\bf So, \: the \: exterior \: angle \: measures \: {140}^{\circ}.}}}}$