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}2118∘
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
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Answers & Comments
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}2118∘
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:
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