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°

Question

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°

Team Careers360 · Accepted Answer

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°.

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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°

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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°