Question

unit 4: the angle sum of a triangle
question 1 find the value of each pronumeral.
question 2 find the value of each pronumeral.
question 3 find the value of each pronumeral.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°.

Step2: Solve for angles in Question 1 - a

Given two angles 65° and 50°. Let the third angle be \(m\). Then \(m=180-(65 + 50)=180 - 115 = 65\).

Step3: Solve for angles in Question 1 - b

Given angles 60° and 70°. Let the third angle be \(a\). Then \(a = 180-(60 + 70)=180 - 130 = 50\).

Step4: Solve for angles in Question 1 - c

Given angles 130° and 25°. Let the third angle be \(c\). Then \(c=180-(130 + 25)=180 - 155 = 25\).

Step5: Solve for angles in Question 1 - d

Given angles 87° and 75°. Let the third angle be \(x\). Then \(x=180-(87 + 75)=180 - 162 = 18\).

Step6: Solve for angles in Question 1 - e

Given angles 54° and 31°. Let the third angle be \(y\). Then \(y=180-(54 + 31)=180 - 85 = 95\).

Step7: Solve for angles in Question 1 - f

Given angles 64° and 48°. Let the third angle be \(a\). Then \(a=180-(64 + 48)=180 - 112 = 68\).

Step8: Solve for angles in Question 2 - a

Given angles 40° and 70°. Let the third angle be \(x\). Then \(x=180-(40 + 70)=180 - 110 = 70\).

Step9: Solve for angles in Question 2 - b

Since the triangle has two equal - length sides, it is isosceles. Let the equal angles be \(x\). Then \(x=\frac{180 - 90}{2}=45\).

Step10: Solve for angles in Question 2 - c

Given angles 20° and 115°. Let the third angle be \(a\). Then \(a=180-(20 + 115)=180 - 135 = 45\).

Step11: Solve for angles in Question 3 - a

Given angles 70° and 69°. Let the third angle be \(x\). Then \(x=180-(70 + 69)=180 - 139 = 41\).

Step12: Solve for angles in Question 3 - b

In the intersecting - lines situation, vertical angles are equal. So \(x = 60\) and \(y = 50\).

Step13: Solve for angles in Question 3 - c

Given angles 42° and 88°. Let the third angle be \(m\). Then \(m=180-(42 + 88)=180 - 130 = 50\).

Step14: Solve for angles in Question 3 - d

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Given an exterior angle of 160° and one non - adjacent interior angle of 70°. Let the other non - adjacent interior angle be \(x\). Then \(x=160 - 70 = 90\).

Step15: Solve for angles in Question 3 - e

Given an exterior angle of 130° and one non - adjacent interior angle of 45°. Let the other non - adjacent interior angle be \(n\). Then \(n=130 - 45 = 85\).

Step16: Solve for angles in Question 3 - f

Since the triangle has two equal - length sides, it is isosceles. Given one angle of 30°. If the 30° angle is the non - equal angle, then \(x=y=\frac{180 - 30}{2}=75\).

Answer:

Question 1:
a. \(m = 65\)
b. \(a = 50\)
c. \(c = 25\)
d. \(x = 18\)
e. \(y = 95\)
f. \(a = 68\)
Question 2:
a. \(x = 70\)
b. \(x = 45\)
c. \(a = 45\)
Question 3:
a. \(x = 41\)
b. \(x = 60,y = 50\)
c. \(m = 50\)
d. \(x = 90\)
e. \(n = 85\)
f. \(x = 75,y = 75\)