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
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.
