Question
Point P is the center of the circle in the figure above. What is the value of x ?
The correct answer is: 80degrees
The value of x is 80.
There can be two method to solve this problem,
Method 1:-
To solve this question we should first know the following theorem
The measure of an angle inscribed in a circle is half the measure of
the central angle that intercepts the same arc.
That is, m BAC = 
Also, the sum of the interior angles of quadrilateral ABCP is 360°,
and the measure of the obtuse angle P will be
360° − x°
Hence, ()° +20° + (360° - x°) + 20° = 360°
Simplifying this equation gives
()° + 400° - x° = 360°
Subtract 400 from both sides we get
- ()° = - 40°
So, ()° = 40°
Multiplying both sides by 2 we get,
x = 80°
Method 2:-
If points A and P are joined, then the triangles that will be formed,
APB and APC,
They are isosceles because
PA = PB = PC.
It follows that the base angles on both triangles each have measure of 20°.
Angle A consists of two base angles,
therefore, 
= 40°
Since the measure of an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc,
Then measure of angle x will be 2(40) = 80°
Related Questions to study
The circle above with center O has a circumference of 36. What is the length of minor arc 
?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
The circle above with center O has a circumference of 36. What is the length of minor arc ?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
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Note:
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