1. Angles in Triangles

2. 6MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.
Objective: Understand how to find the degree measure of an angle in a triangle.
Learning target: Answer at least 3 of the 4 angle questions correctly on the exit ticket.

3. How do the angles of a triangle relate to each other?
Let’s do an activity to try to figure it out

4. Label the 3 angles of your triangle as A, B, and C

5. Tear off each of the corners (yes, really)
Tear off each of the corners (yes, really). Keep the corners, we will be using these.

6. Set aside the middle and just work with the 3 corners
Set aside the middle and just work with the 3 corners. Remember that these corners are the three angles of the triangle. Can you rotate/move them so that they form a shape together?

7. No matter what your triangle looked like or how you tore off the corners, you should be able to form something like this:

8. We showed that the three angles of a triangle can always be rearranged to form this shape.
What does this tell us about the 3 angles of a triangle? Hint: what did they form when rearranged?

9. Since the 3 angles of a triangle combine into a straight angle, that means that the 3 angles of a triangle always add up to 180°

10. How do the angles of a triangle relate to each other?
The sum of the degree measures of the three angles always equals 180°
The measure of an angle is how many degrees it is

11. How can we calculate the degree measure of a triangle’s angle?
What is x?
Set up an equation using the other angles we already know.
Since the sum of a triangle’s angles is 180°, we know 50° + 60° + x = 180°
110° x = 180°
-110° °
x = 70°
Check: 50° + 60° + 70° ?= 180° ° = 180°

12. What is m∠E?
35° + 65° + x = 180°
100° x = 180°
-100° °
x = 80°

13. What is m∠K?
37° + 85° + x = 180°
122° x = 180°
-122° °
x = 58°

14. What is y?
17° + 34° + y = 180°
51° y = 180°
-51° °
y = 129°

15. What is g?
Right angle = 90°
28° + 90° + g = 180°
118° + g = 180°
-118° °
g = 62°

16. What is m∠UWV?
Right angle = 90°
41.3° + 90° + x = 180°
131.3° + x = 180.0°
-131.3° °
x = °

17. What are different types of triangles?
Acute triangles have all acute angles
Right triangles have one right angle.
Obtuse triangles have one obtuse angle.

18. Write your answer
You have may noticed that there are no words for a triangle with 2 right angles or a triangle with 2 obtuse angles. This is because no such triangles exist. Can you explain why?
“A triangle cannot have more than one right or obtuse angle because _______________________________.”
that would make the triangle have more than 180 degrees, which is impossible.