Answer:
x =55 degrees
y = 35 degrees
Step-by-step explanation:
We know that the distance from the center of the circle to the circumference is the radius
that means the triangle starting out from O is isosceles since two of the sides are radii and thus the angle of those sides are the same
Let us call one of the angles z
we know that the sum of the angles in a triangle is 180 degrees
That simply means;
80 + 2z = 180
2z = 180-80
2z = 100
z = 100/2
z = 50 degrees
So the angles at each upper end of the cyclic quadrilateral are;
x + 50 and y + 50
we know that the angles that face each other in a cyclic quadrilateral are supplementary
Thus;
95 + y+ 50 = 180
y= 180-95-50
y= 180-145
y = 35 degrees
Now, for x, the angle supplementary to the angle that faces x+ 50 equals x + 50
Thus;
x + 50 = 105
x= 105-50
x = 55 degrees
The measure of ∠ABP and ∠ABC are 32° and 64° respectively.
<h3>what is a bisector of an angle?</h3>
Any line which divides an angle into two equal halves is a bisector of that angle.
Analysis:
Since the arcs at D and E are drawn with the same radius and arc using center D and E are intersected by line PB( which is the bisector of the full arc with center B) then ∠ABP = ∠PBC = 32°.
∠ABC = ∠ABP + ∠PBC
∠ABC = 32 + 32 = 64°
In conclusion, ∠ABP and ∠ABC are 32° and 64°
Learn more about bisectors of angles: brainly.com/question/24334771
#SPJ1
Answer:
5/12
Step-by-step explanation:
15 to 36 can also be written as 15/36.
Divide by common values to simplify.
15÷3/36÷3
5/12
Best of Luck!
Answer:
1/9
Step-by-step explanation:
3⁻² = 1/3² = 1/9