Question

Given the quadrilateral below, select all of the correct responses.

Answer 1

Step-by-step explanation:

The greatest angle of a cyclic quadrilateral ABCD in which ∠A=(2x−1)

o

,∠B=(y+5)

o

,∠C=(2y+15)

o

and ∠D=(4x−7)

o

is:

Answer

In cyclic quadrilateral, the sum of opposite angles =180

o

⟹∠A+∠C=180

o

⟹2x−1+2y+15=180

o

⟹x+y=83 ...(i).

Also, ∠B+∠D=180

o

⟹4x+y=182 ....(ii).

Then, by solving (i) and (ii),

x=33 and y=50.

Thus, ∠A=65°

,∠B=55°

,∠C=115°

,∠D=125°

.

So, greatest angle ∠D=125°.

Hence, option C is correct.