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

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

Step2: Solve for Question 1a

We know two angles of the triangle are 85° and 50°. Let the third angle be \(m\). Then \(m=180-(85 + 50)=45\).

Step2: Solve for Question 1d

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

Step2: Solve for Question 2a

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

Step2: Solve for Question 2b

Two angles are 45° and 45°. Let the third angle be \(x\). Then \(x=180-(45 + 45)=90\).

Step2: Solve for Question 3a

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

Step2: Solve for Question 3b

We have vertical - angle pairs. \(x = 60\) and \(y = 50\) (vertical angles are equal).

Step2: Solve for Question 3d

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

Step2: Solve for Question 3e

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

Step2: Solve for Question 3f

If one angle is 30° and the triangle is isosceles (assuming the equal angles are \(x\) and \(y\)), and the third angle is \(a\). First, if the non - equal angle is 30°, then \(x=y=\frac{180 - 30}{2}=75\) and \(a = 30\).

Answer:

Question 1a: \(m = 45\)
Question 1d: \(x = 18\)
Question 2a: \(x = 70\)
Question 2b: \(x = 90\)
Question 3a: \(x = 41\)
Question 3b: \(x = 60,y = 50\)
Question 3d: \(x = 90\)
Question 3e: \(n = 85\)
Question 3f: \(x = 75,y = 75,a = 30\)