Question

Tin the adjoining figure P is the circumcenter of triangle ABC if angle apc is equal to 118 degree and angle pbc is equal to 45 degree then find measure of Arc BAC and measure of 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 = $\dfrac{118^{\circ}}{2}$

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

Answer 2

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 = \dfrac{118^{\circ}}{2}

2

118

∘

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