3 Views

Question : In $\triangle $ABC, D is a point on side BC such that $\angle$ADC = 2$\angle$BAD. If $\angle$A = 80° and $\angle$C = 38°, then what is the measure of $\angle$ADB?

Option 1: 58°

Option 2: 62°

Option 3: 52°

Option 4: 56°


Team Careers360 6th Jan, 2024
Answer (1)
Team Careers360 7th Jan, 2024

Correct Answer: 56°


Solution :

Let $\angle$BAD = z then $\angle$ADC = 2z
In $\triangle $ABC,
⇒ $\angle$A + $\angle$B + $\angle$C = 180º
⇒ 80° + $\angle$B + 38° = 180º
⇒ $\angle$B + 118° = 180º
⇒ $\angle$B = 62º
In $\triangle $ABD,
⇒ $\angle$A + $\angle$B = $\angle$ADC (The sum of two opposite angles is equal to the external angle)
⇒ z + 62º = 2z
⇒ z = 62º
And,
⇒ $\angle$ABD + $\angle$BAD + $\angle$ADB = 180º
⇒ 62º + 62º + $\angle$ADB = 180º
⇒ $\angle$ADB = 180º – 124º = 56º
Hence, the correct answer is 56º.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

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
GRE ® Registrations 2024
Apply
Apply for GRE® Test now & save 10% with ApplyShop Gift Card | World's most used Admission Test for Graduate & Professional Schools
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