Copyright © by Holt, Rinehart and Winston
Reteach
Angle Relationships in Triangles
According to the Triangle Sum Theorem, the sum of the angle
measures of a triangle is 1808.
m∠J ( m∠K ( m∠L ( 62° ( 73° ( 45°
( 180°
The corollary below follows directly from the Triangle Sum Theorem.
Use the figure for Exercises 1 and 2.
1. Find m∠ABC.
2. Find m∠CAD.
Use (RST for Exercises 3 and 4.
3. What is the value of x?
4. What is the measure of each angle?
What is the measure of each angle?
[pic] [pic] [pic]
5. ∠L 6. ∠C 7. ∠W
Reteach
Angle Relationships in Triangles continued
An exterior angle of a triangle is formed by
one side of the triangle and the extension of
an adjacent side.
∠1 and ∠2 are the remote interior angles of
∠4 because they are not adjacent to ∠4.
Find each angle measure.
[pic] [pic]
8. m∠G 9. m∠D
Find each angle measure.
[pic] [pic]
10. m∠M and m∠Q 11. m∠T and m∠R
Reteach
1. 47° 2. 38°
3. 14
4. m(R ( 85°; m(S ( 30°; m(T ( 65°
5. 49° 6. 39.8°
7. (90 ( x)° 8. 51°
9. 41° 10. 82°; 82°
11. 33°; 33°
-----------------------
|Corollary |Example |
|The acute angles of a right | |
|triangle are complementary. | |
| | |
| |[pic] |
| |m∠C ( m∠E ( 90° |
m∠C ( 90° ( 39°
( 51°
|Exterior Angle Theorem |
|The measure of an exterior angle of a |
|triangle is equal to the sum of the |
|measures of its remote interior angles. |
|Third Angles Theorem |
|If two angles of one triangle are congruent |
|to two angles of another triangle, then |
|the third pair of angles are congruent. |
m∠4 ’ m∠1 + m∠2
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