Question

p is a point on the circle of diameter AB .in angle ABP ,are angle A ,angel B are complementary angle ? give reasons ​

Answer 1

Answer:

YES.

Step-by-step explanation:

We know that,

the angle subtended by the diameter on the circle is 90°.

Therefore,

In triangle ABP,

<APB = 90° ------ (1)

Again,

we know that,

Sum of the angle of a triangle = 180°

=> <PAB + <ABP + <APB = 180°

=> <PAB + <ABP +90° = 180° ----from (1)

=> <PAB + <ABP = 180°- 90°

or <A + <B = 90°

Hence, <A and <B are complementary angles.