Triangle Sum Theorem

Triangle Sum Theorem

​Read:

​Let Me Show You:

All angles in a triangle add up to be 180 degrees.

70
50
+60
180

​Sometimes Triangles have missing angles....

​To solve for missing angles:
1. create an equation. (add all angles to equal 180)
2. Solve for the value of x.

3. Check your work: Plug values back into the triangle.

​Show my work:
1. x + x+ 110 = 180
2. 2x +110 = 180
-110 -110
2x = 70
2 2
x = 35 degrees

​3. Check:
35 + 35 +110 = 180 degrees

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°
• 90°
• 180°
• 360°

Multiple Choice

Find the measure of the indicated angle.

• $$135\degree$$  

• $$55\degree$$  

• $$45\degree$$  

• $$60\degree$$  

Multiple Choice

Find the measure of the indicated angle.

• $$30\degree$$  

• $$25\degree$$  

• $$155\degree$$  

• $$65\degree$$  

Multiple Choice

Find the measure of the indicated angle.

• $$45\degree$$  

• $$33\degree$$  

• $$123\degree$$  

• $$147\degree$$  

Multiple Choice

Find the measure of the indicated angle.

• $$90\degree$$  

• $$71\degree$$  

• $$98\degree$$  

• $$82\degree$$   

Multiple Choice

Find the measure of the indicated angle.

• $$56\degree$$  

• $$118\degree$$   

• $$28\degree$$  

• $$62\degree$$  

Multiple Choice

Find the measure of the missing angle.

• 90^o
• 10⁰
• 130^o
• 50^o

Multiple Choice

Find the measure of each angle indicated.

• 50
• 20
• 29
• 48

Multiple Choice

If two angles in a triangle are $$45\degree$$  and $$\ 75\degree$$ , what is the measure of the third angle?

• $$75\degree$$  

• $$90\degree$$  

• $$60\degree$$  

• $$70\degree$$  

Multiple Choice

Find the value of k.

• $$66$$  

• $$57$$  

• $$114$$  

• $$22$$  

Multiple Choice

Solve for x.

• 16
• 11
• 50
• 6

Multiple Choice

Solve for x.

• 7
• 9
• -11
• -8

Multiple Choice

Solve for x.

• 6
• 5
• -11
• 4

Multiple Choice

What is the third angle of a triangle whose 1st angle is 79 and the 2nd angle is 43?

• 43
• 58
• 72
• 101

Multiple Choice

A triangle has angle measurements of (x + 3), 2x, and (7x + 7). Write an equation to represent the situations and solve for x.

• x = 17

• x = 20

• x = 25

• x = 12

Multiple Choice

A triangle has angle measurements of (x + 3), 2x, and (7x + 7). Which angle is the smallest angle?

• (x + 3) = 20

• (7x + 7) =126

• (2x) = 34

• There is no smaller angle