Question

if an exterior angle of a triangle is 140°and it's opposite interior angles are equal to each other, which of the following is the measure of the equal angles angles of the triangle?​

Answer 1

Step-by-step explanation:

• Given the exterior angle = 140°
• Interior opposite angle are equal.

Let one of the interior opposite angle be x.

Then x + x = 140°.

[∵ Exterior angle = sum of interior

opposite angles]

• =⟩ 2x = 140°

• =⟩ x = 140°/2

• =⟩ x = 70°

Interior opposite angle = 70°, 70°.

Sum of the three angles of a triangle = 180°.

• 70° + 70° + Third angle = 180°

• 140° + Third angle = 180°

• Third angle = 180° – 140° = 40°

∴ Interior angle are 40°, 70°, 70°.

$hope \: i t \: helps \: you$

Answer 2

★ How to do :-

Here, we are given that the exterior angle of a triangle measures 140° and it's interior opposite angles measures the same compared to each other. We are asked to find the measurements of all the angles of the triangle. As we know that the exterior angle always measures as the sum of it's interior opposite angles. This concept is known as exterior angle property of a triangle. To find the all angles of the triangle we use an other concept called as the angle sum property of the triangle. This property says that all the angles in a triangle always adds up to 180°. If not, then it cannot form a triangle. Using these two concepts, we can solve this question. So, let's solve!!

$\:$

➤ Solution :-

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

Substitute the given values.

${\tt \leadsto x + x = {140}^{\circ}}$

Add both variables on LHS.

${\tt \leadsto 2x = {140}{\circ}}$

Shift the number 2 from LHS to RHS.

${\tt \leadsto x = \dfrac{140}{2}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = {70}^{\circ}}$

$\:$

Now, let's find the third side of the triangle.

Third angle of the triangle :-

${\sf \longrightarrow \underline{\boxed{\sf Angle \: sum \: property = {180}^{\circ}}}}$

Substitute the given values.

${\tt \leadsto {70}^{\circ} + {70}^{\circ} + y = {180}^{\circ}}$

Add the values on LHS.

${\tt \leadsto 140 + y = 180}$

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

${\tt \leadsto y = 180 - 140}$

Subtract the values to get the third angle.

${\tt \leadsto y = {40}^{\circ}}$

$\:$

${\red{\underline{\boxed{\bf So, \: all \: angles \: of \: triangle \: are \: {70}^{\circ}, \: {70}^{\circ} \: and \: {40}^{\circ}.}}}}$