Question

The measure of the exterior angle of a triangle are 140° and 130° respectively . Which type of triangle

Answer 1

Question :--- The measure of the exterior angle of a triangle are 140° and 130° respectively . Which type of triangle ?

Concept used :--

→ Sum of Exterior angle of a ∆ and its interior angle is 180° . ( As both are on a straight line ) .

→ Sum of all three angles's of a ∆ is 180° .

→ A ∆ is said to be right ∆ , when one of its angle is Equal to 90°..

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❁❁ Refer To Image First .. ❁❁

From image , we can see that, Exterior angle on point A is 140° .

So,

→ Angle BAC ( interior angle) = 180°-140° = 40° .

SImilarly,

→ Angle ABC ( interior angle) = 180° - 130° = 50° .

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Now, we have Two angles of ∆ABC.

we know that,

→ Angle ABC + angle BAC + angle ACB = 180° (Angle sum property.)

Putting values ,

→ 40° + 50° + angle ACB = 180°

→ 90° + angle ACB = 180°

→ angle ACB = 180° - 90°

→ angle ACB = 90°.

So, if one angle of ∆ABC is 90° , this triangle is known as right angled triangle.

Hence, we can say That, ∆ABC is a right angled triangle.