The value of each measure based on the incenter is illustrated below.
<h3>What is incenter?</h3>
The incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle. This point is equidistant from the sides of a triangle.
Angle ARU = 40 degree
Length of AU = 20
Angle QPA = 35 degree
Since, AR is angle bisector of angle URK.
So, ∠ARU = ∠ARK = 40 degree
Since, incenter point is equidistant from the sides of a triangle.
So, AT = AU = AK = 20
Since, PA is angle bisector of angle QPU.
So, ∠QPA = ∠UPA
3x + 2 = 4x - 9
4x - 3x = 9 + 2
x = 11
Substituting value of x in angle 3x + 2
We get, ∠QPA = 3(11) + 2 = 35°
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Answer:
The correct option is;
An isosceles trapezoid with legs of length 8
Step-by-step explanation:
The correct option is an isosceles trapezoid with legs of length 8
The given properties of the quadrilateral are;
1) One pair of equal opposite sides
2) One pair of parallel opposite sides
From the given options, the two options which are not parallelograms are the kite and the trapezoid
However given that the option of the kite has a pair of adjacent side of length 8, with the given pair of equal length opposite side of length 8, we have that all the sides of the quadrilateral will be of length 8, and the figure cannot be a kite
An isosceles trapezoid of leg length 8 has one pair of equal length opposite sides of length 8 and one pair of parallel sides of unequal length
Given that the length of the lines that make up the pair of opposite parallel sides in the figure are not specified, the figure can be described by as being an isosceles trapezoid.
<h3>
Answer: D) 72</h3>
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Work Shown:
Angle PQR = (far arc - near arc)/2
2x+72 = ( (2x+252) - (2x+108) )/2
2x+72 = 144/2
2x+72 = 72
2x = 72-72
2x = 0
x = 0/2
x = 0
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Angle PQR = 2x+72
Angle PQR = 2(0)+72
Angle PQR = 72 degrees
