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Find The Measure Of Each Angle Of APQR. 1. M 2QPR=87; M 2Q= 63 2. M ZQPR = 5x; M ZQ =…

Find The Measure Of Each Angle Of APQR. 1. M 2QPR=87; M 2Q= 63 2. M ZQPR = 5x; M ZQ =…

Find the measure of each angle of APQR. 1. m 2QPR=87; m 2Q= 63 2. m ZQPR = 5x; m ZQ = 7x; m ZQPR = 8x – 20 3. ZQPR is a right angle; m 2Q=53 4. m 2QPR= 4x+7; m ZQRP= 3(x-2); m 21= 85 5. m 2QPR = 8x; m 2Q= 7x; m 22= 2(x+65) 2 R P​

Answer:

To find the measure of each angle of APQR, let’s assign variables to the given angles and solve the equations:

Given:

m∠2QPR = 87

m∠2Q = 63

We need to find the measure of each angle. Let’s assume m∠P = x.

Then, we can set up the equation:

m∠2QPR + m∠2Q + m∠P = 180 (since the angles of a triangle add up to 180 degrees)

Substituting the given values:

87 + 63 + x = 180

Solving for x:

x = 180 – (87 + 63)

x = 180 – 150

x = 30

Therefore, m∠P = 30 degrees.

Given:

m∠ZQPR = 5x

m∠ZQ = 7x

m∠ZQPR = 8x – 20

We need to find the measure of each angle. Let’s assume m∠P = y.

Then, we can set up the equations:

m∠ZQPR + m∠ZQ + m∠P = 180 (since the angles of a triangle add up to 180 degrees)

5x + 7x + y = 180 (equation 1)

m∠ZQPR = 8x – 20

8x – 20 = 5x (equation 2)

Solving equation 2 for x:

8x – 5x = 20

3x = 20

x = 20/3

Substituting x in equation 1:

5(20/3) + 7(20/3) + y = 180

100/3 + 140/3 + y = 180

(100 + 140)/3 + y = 180

240/3 + y = 180

80 + y = 180

y = 180 – 80

y = 100

Therefore, m∠P = 100 degrees.

Given:

m∠ZQPR is a right angle (90 degrees)

m∠2Q = 53

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We need to find the measure of each angle. Let’s assume m∠P = z.

Then, we can set up the equation:

m∠ZQPR + m∠2Q + m∠P = 180 (since the angles of a triangle add up to 180 degrees)

90 + 53 + z = 180

143 + z = 180

z = 180 – 143

z = 37

Therefore, m∠P = 37 degrees.

Given:

m∠2QPR = 4x + 7

m∠ZQRP = 3(x – 2)

m∠21 = 85

We need to find the measure of each angle. Let’s assume m∠P = w.

Then, we can set up the equations:

m∠2QPR + m∠ZQRP + m∠P + m∠21 = 360 (since the angles of a quadrilateral add up to 360 degrees)

4x + 7 + 3x – 6 + w + 85 = 360

7x + w + 86 = 360

w = 360 – 7x – 86

w = 274 – 7x

Therefore, the measure of ∠P is 274 – 7x degrees.

Given:

m∠2QPR = 8x

m∠2Q = 7x

m∠22 = 2(x + 65)

We need to find the measure of each angle. Let’s assume m∠P = v.

Then, we can set up the equation:

m∠2QPR + m∠2Q + m∠P + m∠22 = 360 (since the angles of a quadrilateral add up to 360 degrees)

8x + 7x + v + 2(x + 65) = 360

Simplifying the equation:

8x + 7x + v + 2x + 130 = 360

17x + v + 130 = 360

v = 360 – 17x – 130

v = 230 – 17x

Therefore, the measure of ∠P is 230 – 17x degrees.

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