5 Views

Question : ABCD is a cyclic quadrilateral and AD is a diameter. If $\angle$ DAC = 55$^\circ$ then value of $\angle$ABC is:

Option 1: 55$^\circ$

Option 2: 35$^\circ$

Option 3: 145$^\circ$

Option 4: 125$^\circ$


Team Careers360 14th Jan, 2024
Answer (1)
Team Careers360 18th Jan, 2024

Correct Answer: 145$^\circ$


Solution :
Given, a cyclic quadrilateral ABCD and diameter AD
And, $\angle$ DAC = 55$^\circ$
In $\triangle$ ACD,
$\angle$ DAC = 55$^\circ$
$\angle$ ACD = 90$^\circ$ (angle in a semicircle)
$\angle$ ADC = 180$^\circ$ – 55$^\circ$ – 90$^\circ$ = 35$^\circ$ (angle sum property)
We know that opposite angles in a cyclic quadrilateral are supplementary.
So, $\angle$ ABC+ $\angle$ ADC = 180$^\circ$
Or, $\angle$ ABC = 180$^\circ$ – 35$^\circ$ = 145$^\circ$
Hence, the correct answer is 145$^\circ$.

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
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