2 Views

Question : ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and $\angle A D C=148^{\circ}$. What is the measure of the $\angle BAC$?

Option 1: $32^{\circ}$

Option 2: $45^{\circ}$

Option 3: $58^{\circ}$

Option 4: $60^{\circ}$


Team Careers360 18th Jan, 2024
Answer (1)
Team Careers360 20th Jan, 2024

Correct Answer: $58^{\circ}$


Solution :
ABCD is a cyclic quadrilateral.
$\angle ADC = 148^\circ$
The angle formed by drawing lines from the ends of the diameter of a circle to its circumference forms a right angle.
The sum of opposite angles of the cyclic quadrilateral is 180$^\circ$
In quadrilateral ABCD,
$\angle ADC+\angle CBA = 180^\circ$
⇒ $148^\circ+\angle CBA = 180^\circ$
⇒  $\angle CBA = 180^\circ - 148^\circ$
⇒  $\angle CBA = 32^\circ$
In $\triangle ABC$,
$\angle BAC + 90^\circ + \angle CBA = 180^\circ$
⇒ $\angle BAC + 90^\circ + 32^\circ = 180^\circ$
⇒ $\angle BAC + 122^\circ = 180^\circ$
⇒ $\angle BAC = 180^\circ - 122^\circ$
⇒ $\angle BAC = 58^\circ$
$\therefore$ The measure of the ∠BAC is 58°
Hence, the correct answer is 58$^\circ$

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