1. Find the number of degrees in the third angle of the triangle.
2. An architect is designing a home. What is the measure of the missing angle of the roof?
3. There is a slide in the back of the school. The stairs for the slide go straight up. The angle made with the slide and the ground is 49°. What is the value of x?
4. Mental Math Find the value of the missing angle of the right triangle.
5. In △ QRS, m ∠ R is 20° more than m ∠ Q and m ∠ S is 70° more than m ∠ Q. Find m ∠ R.
6. For the figure, find the value of the variable x and m∠Q.
7.
a. Writing If the measures of two angles of a triangle are 100° and 19°, what is the measure of the third angle?
b. Explain how a straight angle is related to the angles of a triangle.
8. Reasoning An art class is designing a sign to put by the entrance to the school. The sign is in the shape of a triangle and has one angle that is 87° and another which is 42°.
a. What is the measure of the third angle?
b. Explain how you could determine if the triangle is acute, right, or obtuse without finding the third angle.
9. Error Analysis On a math test the students are given a right triangle. One of the acute angles has a measure of 55°. One student says that the measure of the other acute angle is 125°.
a. What is the measure of the other acute angle?
b. What error might the student have made?
A. The student only subtracted the right angle from 180°.
B. The student subtracted the sum of the two given angles from 360°.
C. The student added the right angle and the given acute angle, but did not subtract the sum from 180°.
D. The student only subtracted the acute angle from 180°.