Question

In the adjoining figure,
P is the circumcentre of the
triangle ABC ,measure of angle APC =118, measure angle PBC =45 . then find 1) m( arc BXC ) 2) m(arc BCA )​

Answer 1

Answer:

The measure of arc ∠ ACB is  59°

The measure of arc ∠ BAC is 63°

Step-by-step explanation:

Given as :

In the figure shown , A circumference with center P

∠ APC = 118°

∠ PBC = 45°

Let The measure of arc BAC = x°

The measure of arc BCA = y°

According the question

∠ APC = 2 ∠ ABC

Or, ∠ ABC =  

i.e ∠ ABC = 59°

∵  ∠ ABC =  ∠ ABP +  ∠ CBP

So,   ∠ ABP =   ∠ ABC  -   ∠ CBP

Or,  ∠ ABP =  59° -  45°

∴ ∠ ABP =  14°

Since The triangle is isosceles

So, ∠ ACB = ∠ ABC = 59°

So, The measure of arc  ∠ ACB =  59°

Again

Since The sum of angle of triangle = 180°

∠ BAC = 180° - 118°

∠ BAC = 63°

The measure of arc ∠ BAC = 63°

Hence, The measure of arc ∠ ACB is  59°

And The measure of arc ∠ BAC is 63° Answer