1. Get out a pencil and 2 pieces of paper.
SILENTLY (that means without talking)…
Get out a pencil and 2 pieces of paper.
Start working on your warm-ups.

2. Learning Target: Students can find unknown angles in triangles.
Math 8
Day 17
Learning Target: Students can find unknown angles in triangles.

3. Vocabulary Triangle Sum Theorem acute triangle right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle

4. Draw a triangle and extend the bottom side
Draw a triangle and extend the bottom side. Then draw a line parallel to the extended side, as shown.
The sides of the triangle are transversals to the parallel lines.
The three angles in the triangle can be arranged to form a straight line or 180°.

5. An acute triangle has 3 acute angles
An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

6. Example 1:
Find p° in the acute triangle.
73° + 44° + p° = 180°
117° + p° = 180°
–117° –117°
p° = 63°

7. Example 2:
Find c° in the right triangle.
42° + 90° + c° = 180°
132° + c° = 180°
–132° –132°
c° = 48°

8. Example 3:
Find m° in the obtuse triangle.
23° + 62° + m° = 180°
85° + m° = 180°
–85° –85°
m° = 95°

9. Example 4:
Find a° in the acute triangle.
88° + 38° + a° = 180°
38°
126° + a° = 180°
–126° –126°
a° = 54° a°
88°

10. Example 5:
Find b in the right triangle.
38°
38° + 90° + b° = 180°
128° + b° = 180°
–128° –128°
b° = 52° b°

11. Example 6:
Find c° in the obtuse triangle.
24° + 38° + c° = 180°
38°
62° + c° = 180°
24° c°
–62° –62°
c° = 118°

12. Interior Angles Theorem:
The sum of the interior angles of a triangle is ________°

13. An equilateral triangle has 3 congruent sides and 3 congruent angles.
An isosceles triangle has at least 2 congruent sides and 2 congruent angles.
A scalene triangle has no congruent sides and no congruent angles.

14. Example 7:
Find the angle measures in the isosceles triangle.
62° + t° + t° = 180°
Triangle Sum Theorem
62° + 2t° = 180°
Combine like terms.
–62° –62°
Subtract 62° from both sides.
2t° = 118°
2t° = 118°
Divide both sides by 2.
t° = 59°
The angles labeled t° measure 59°.

15. Find the angle measures in the scalene triangle.
Example 8:
Find the angle measures in the scalene triangle.
2x° + 3x° + 5x° = 180°
Triangle Sum Theorem
10x° = 180°
Combine like terms.
Divide both sides by 10.
x = 18°
The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

16. Ticket Out the Door
1. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°.
2. Find the missing angle measure in an obtuse triangle with angle measures of 10° and 15°.