20 Views

Question : $\triangle ABC$ is an equilateral triangle. The side $BC$ is produced to point $D$. If $A$ joines $D$ and $B C=CD$, then the degree measure of angle $CAD$ is equal to:

Option 1: $30^{\circ}$

Option 2: $15^{\circ}$

Option 3: $45^{\circ}$

Option 4: $18^{\circ}$


Team Careers360 10th Jan, 2024
Answer (1)
Team Careers360 18th Jan, 2024

Correct Answer: $30^{\circ}$


Solution :
Given: BC = CD
And ABC is an equilateral triangle.
$\therefore$ AB = BC = CA
$\angle ACB = \angle ABC = \angle BAC = 60°$
To find $\angle CAD$
$\angle ACB + \angle ACD = 180°$
⇒ $ \angle ACD = 180°-60°$
⇒ $\angle ACD = 120°$
$\triangle ACD$ is an isosceles triangle
$\therefore$ $\angle CAD = \angle ADC$
$\angle CAD + \angle ACD + \angle ADC = 180°$
⇒ $\angle CAD + 120° + \angle ACD = 180°$
⇒ $2\angle CAD = 60°$
⇒ $\angle CAD = 30°$
Hence, the correct answer is $30^{\circ}$.

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