✓ Lesson Check

Do you know HOW?

Find the measure of the third angle of a triangle given the measures of two angles.

1. 34 and 88
2. 45 and 90
3. 10 and 102
4. x and 50

In a triangle, ∠ 1 angle 1  is an exterior angle and ∠ 2 angle 2  and ∠ 3 angle 3  are its remote interior angles. Find the missing angle measure.

5. m ∠ 2 = 24 m angle , 2 equals 24  and m ∠ 3 = 106 m angle , 3 equals 106
6. m ∠ 1 = 70 m angle , 1 equals 70  and m ∠ 2 = 32 m angle , 2 equals 32

Do you UNDERSTAND?

7. Explain how the Triangle Exterior Angle Theorem makes sense based on the Triangle Angle-Sum Theorem.
8. Error Analysis The measures of the interior angles of a triangle are 30, x, and 3x. Which of the following methods for solving for x is incorrect? Explain.

   1. x + 3 x = 30 4 x = 30 x = 7.5 table with 3 rows and 2 columns , row1 column 1 , x plus 3 x , column 2 equals 30 , row2 column 1 , 4 x , column 2 equals 30 , row3 column 1 , x , column 2 equals 7.5 , end table

   2. x + 3 x + 30 = 180 4 x + 30 = 180 4 x = 150 x = 37.5 table with 4 rows and 2 columns , row1 column 1 , x plus 3 x plus 30 , column 2 equals 180 , row2 column 1 , 4 x plus 30 , column 2 equals 180 , row3 column 1 , 4 x , column 2 equals 150 , row4 column 1 , x , column 2 equals , 37.5 , end table