Question

If AB is a chord of a circle, P and Q are the two points on the circle different form A and B. Then prove that angle APB+ angle AQB=180 degrees or Angle APB= angle AQB

Answer 1

when we join PA, PB,QB and QA.
∠APB and∠BQA are two angles made by chord ABin the same segment APQB of circle.Then by using theorem:
angles in the same segment of a circle are equal.
So therefore ∠APB=∠BQA
                                             

Answer 2

Proved below.

Step-by-step explanation:

Given:

Here, AB is a chord of a circle.

P and Q are the two points on the circle different form A and B.  

As shown in thew figure below we have two cases,

Let ∠ APB = x, AQB = y

Case 1,

∠ APB = arc AB, ∠ AQB = arc AB             [Angles to its opposite arc are equal]

⇒ ∠ APB = ∠ AQB

Case 2,

Here AQBP is a cyclic quadrilateral.

⇒ ∠ APB + ∠ AQB = 180°

Hence proved.