Question

There was a circular park in a colony. For fencing purpose po les A, B, C and D were erected at the circumference ofthe park.
Wires were tied from A to B, B to C, and C to D. A rope was tied frompole D to A temporarily. It was found that∠A=100oand∠D=80o.
what is the value of angle ABC

Answer 1

Circle

Given:

A,B,C and D are the poles erected on the circumference of circular park.

∠$A=100$°  and ∠$D=80$°.

To find:

Value of ∠ABC

Explanation:

Cyclic Quadrilateral: It is a quadrilateral which is inscribed in a circle, which means there is a circle that passes through all four vertices of the quadrilateral. It has several properties such as:

• All vertices of quadrilateral lie on the circumference of the circle.
• The sum of pair of opposite angles are 180°.
• The measure of an exterior angle at a vertex is equal to the opposite interior angle.

According to this question,

the figure associated with  this is  attached,

ABCD will form Cyclic Quadrilateral,

and ∠A is opposite to ∠C

and ∠B is opposite to ∠D.

So, according to property of cyclic quadrilateral,

∠B + ∠D= 180°

∠B $+80$°$=180$°

∠B =$100$°

So, ∠ABC = 100°

Answer 2

Answer:

the answer is 100

Step-by-step explanation:

angle A is opp. to angle C , and

angle B is opp. to angle D.

angle B + angle D =180* (prop.of cyclic quad)

angle B + 80 =180

angle B =100

thus, angle ABC =100⁰

HOPE IT HELPS<3