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$^\circ$
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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$^\circ$ $\therefore$ The measure of the largest angle of the triangle is 76$^\circ$. Hence, the correct answer is 76$^\circ$.
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