Question : Three consecutive angles of a cyclic quadrilateral are in the ratio of 1 : 4 : 5. The measure of the fourth angle is:
Option 1: 120°
Option 2: 60°
Option 3: 30°
Option 4: 80°
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: 60°
Solution :
Given: Three consecutive angles of a cyclic quadrilateral are in the ratio of 1 : 4 : 5.
We know that the sum of the opposite angles of a cyclic quadrilateral is 180°.
Let $\angle A=x°, \angle B=4x°,$ and $\angle C=5x°$.
Since $\angle A+ \angle C=180°$.
So, $x+5x=180°$
⇒ $6x=180°$
⇒ $x=30°$
Since $\angle B+ \angle D=180°$
So, $4x+\angle D=180°$
⇒ $4×30°+\angle D=180°$
⇒ $120°+\angle D=180°$
⇒ $\angle D=180°-120°$
⇒ $\angle D=60°$
So, the measure of the fourth angle is 60°.
Hence, the correct answer is 60°.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
