In the given figure AB = AC and then is equal to <img width="110" height="90" src="https://gradeup-question-images.grdp.co/liveData/PROJ30935/1557745512141658.png" style="line-height: 1.4; border-style: none; max-width: 100%; position: relative; overflow: hidden; color: rgb(11, 24, 47); font-family: "nunito sans", poppins, sans-serif; font-size: 19.2px; vertical-align: middle;" alt="" /> - In the given figure AB = AC and then is equal to <img width="110" height="90" src="https://gradeup-question-images.grdp.co/liveData/PROJ30935/1557745512141658.png" style="line-height: 1.4; border-style: none; max-width: 100%; position: relative; overflow: hidden; color: rgb(11, 24, 47); font-family: "nunito sans", poppins, sans-serif; font-size: 19.2px; vertical-align: middle;" alt="" />

Mathematics : Math Misc

In the given figure AB = AC and then is equal to

A. 60o

B. 105o

C. 30o

D. 75o

Correct Answer :

C. 30o

Explanation

In triangle ABC, AB=AC implies that ABC is an isosceles triangle Let one of its equal angle be x then , x +x+∠A = 180° (Angle Sum Property) ⇒ 2x + ∠A = 180° ...... EQ.1 Also ,∠A+x = 105° (exterior angle property) Multiplying the above equation by 2 we get , 2∠A+2x = 210° ......... EQ. 2 Subtracting EQ. 2 from EQ.1 , 2∠A + 2x -2x -∠A= 210°-180° ⇒ ∠A = 30°