2. Trapezoid PQRS given below is an isosceles trapezoid. Find mzP, mzQ and mR.
S
R
P Р
Q
pls. help me I really need this rn
S
R
P Р
Q
pls. help me I really need this rn
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Problem 1 :
Trapezoid PQRS given below is an isosceles trapezoid.
Find m∠P, m∠Q and m∠R.
Problem 2 :
Prove that the figure ABCD given below is a trapezoid.
Problem 3 :
A baker is making a cake like the one which is given below. The top layer of the cake has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer of the cake be ?
Detailed Answer Key
Problem 1 :
Trapezoid PQRS given below is an isosceles trapezoid.
Find m∠P, m∠Q and m∠R.
Solution :
Given : PQRS is an isosceles trapezoid.
According to theorem on trapezoids, each pair of base angles in an isosceles trapezoid must be congruent.
So, we have
m∠S = m∠R = 50°
Because ∠S and ∠P are consecutive interior angles formed by parallel lines, they are supplementary.
So, we have
m∠S + m∠P = 180°
Substitute m∠S = 50°.
50° + m∠P = 180°
Subtract 50° from both sides.
m∠P = 130°
According to theorem on trapezoids, each pair of base angles in an isosceles trapezoid must be congruent.
So, we have
m∠P = ∠Q = 130°
Hence,
∠P = 130°
∠Q = 130°
∠R = 50°
Problem 2 :
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WORKSHEET ON TRAPEZOIDS
Problem 1 :
Trapezoid PQRS given below is an isosceles trapezoid.
Find m∠P, m∠Q and m∠R.
Problem 2 :
Prove that the figure ABCD given below is a trapezoid.
Problem 3 :
A baker is making a cake like the one which is given below. The top layer of the cake has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer of the cake be ?
Detailed Answer Key
Problem 1 :
Trapezoid PQRS given below is an isosceles trapezoid.
Find m∠P, m∠Q and m∠R.
Solution :
Given : PQRS is an isosceles trapezoid.
According to theorem on trapezoids, each pair of base angles in an isosceles trapezoid must be congruent.
So, we have
m∠S = m∠R = 50°
Because ∠S and ∠P are consecutive interior angles formed by parallel lines, they are supplementary.
So, we have
m∠S + m∠P = 180°
Substitute m∠S = 50°.
50° + m∠P = 180°
Subtract 50° from both sides.
m∠P = 130°
According to theorem on trapezoids, each pair of base angles in an isosceles trapezoid must be congruent.
So, we have
m∠P = ∠Q = 130°
Hence,
∠P = 130°
∠Q = 130°
∠R = 50°