Question : In $\triangle ABC, \angle B = 60^\circ$ and $\angle C = 40^\circ$, AD and AE are respectively the bisectors of $\angle A$ and perpendicular on BC. Find the measure of $\angle EAD$.

Option 1: $11^\circ$

Option 2: $10^\circ$

Option 3: $12^\circ$

Option 4: $9^\circ$


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

Correct Answer: $10^\circ$


Solution :
Given: In $\triangle ABC$, $\angle B = 60^\circ$ and $\angle C = 40^\circ$.
We know that,
$\angle BAC+\angle ABC+\angle ACB=180^\circ$
⇒ $\angle BAC = 180^\circ-60^\circ-40^\circ$
⇒ $\angle BAC = 80^\circ$
Since AD is the angle bisector of $\angle BAC$ in $\triangle ABC$
$\therefore \angle BAD = \frac{80^\circ}{2}=40^\circ$
Now, in $\triangle AEB$
$\angle BAE+\angle ABE+\angle AEB=180^\circ$
⇒ $\angle BAE = 180^\circ-60^\circ-90^\circ$
⇒ $\angle BAE = 30^\circ$
⇒ $\angle EAB = 30^\circ$
$\therefore \angle EAD=\angle BAD-\angle EAB=40^\circ-30^\circ=10^\circ$
Hence, the correct answer is $10^\circ$.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books