Question : The exterior angles obtained on producing the base of a triangle both ways are 121$^\circ$ and 104$^\circ$. What is the measure of the largest angle of the triangle?
Option 1: 75$^\circ$
Option 2: 76$^\circ$
Option 3: 74$^\circ$
Option 4: 66$^\circ$

Question

Question : The exterior angles obtained on producing the base of a triangle both ways are 121$^\circ$ and 104$^\circ$. What is the measure of the largest angle of the triangle?

Option 1: 75$^\circ$

Option 2: 76$^\circ$

Option 3: 74$^\circ$

Option 4: 66$^\circ$

Team Careers360 · Accepted Answer

Correct Answer: 76$^\circ$

Solution : First exterior angle = 121$^\circ$
Second exterior angle = 104$^\circ$
The sum of all the exterior angles of a triangle is 360$^\circ$
Let the three interior angles be A, B, and C and the third exterior angle be x
⇒ 121$^\circ$ + 104$^\circ$ + x = 360$^\circ$
⇒ x = 360$^\circ$ - 225$^\circ$
⇒ x = 135$^\circ$
Largest interior angle = supplement of smallest exterior angle
Smallest exterior angle = 104$^\circ$
Measure of the largest angle of the triangle = 180$^\circ$ - 104$^\circ$ = 76$^\circ$
$ herefore$ The measure of the largest angle of the triangle is 76$^\circ$.
Hence, the correct answer is 76$^\circ$.

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Question : The exterior angles obtained on producing the base of a triangle both ways are 121∘ and 104∘. What is the measure of the largest angle of the triangle?Option 1: 75∘Option 2: 76∘Option 3: 74∘Option 4: 66∘

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Question : The exterior angles obtained on producing the base of a triangle both ways are 121 $^{\circ}$ and 104 $^{\circ}$ . What is the measure of the largest angle of the triangle?
Option 1: 75 $^{\circ}$
Option 2: 76 $^{\circ}$
Option 3: 74 $^{\circ}$
Option 4: 66 $^{\circ}$