Question

The points A,B,C,D,E are marked on the circumfeence of a circle in clockwise direction such that angle ABC = 130° and angle CDE = 110°. the measure of angle ACE in degrees is greater than or equal to:

(A) 50°

(B) 60°

(C) 70°

(D) 80°

Answer 1

60°
Because,

EDC+DCB+CBA= 360°
110+DCB+130= 360°
DCB=360°-240
DCB=60

Answer 2

Answer:

B.$60^{\circ}$

Step-by-step explanation:

We are given that points A,B,C,D and E are marked on the circumference

We are given that angle AB=130 degrees

angle CDE=110 degrees

We have to find the value of angle ACE

Angle ABC+ angle AEC=$180^{\circ}$

In cyclic quadrilateral ABCE, sum of diagonally opposite angles 180 degrees

130+angle AEC=180

Angle AEC=180-130=50 degrees

In cyclic quadrilateral ACDE

angle CDE+ angle EAC=180

110+Angle EAC=180

Angle EAC =180-110=70 degrees

In triangle AEC

angle EAC+Angle ECA+angle AEC=180 ( angle sum property of triangle )

70+Angle ACE+50=180

Angle ACE+120=180

Angle ACE=180-120=60 degrees

Hence, the measure of angle equals to 60 degrees.

Option B is true.