Angles

Angles

G.4: Use visualization, spatial reasoning, and geometric modeling to solve problems. 7.G.4.2 Identify and describe the properties of two-dimensional shapes b. use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle

Teacher

Missing angles-Students need to make the connection that the total degrees in a triangle are 180. There are two triangles in every rectangle. Rectangles have to have four right angles that are each 90 degrees which is a total of 360 degrees. When a rectangle is divided on the diagonal it divides the right angle in half creating two 45 degree angles. Each triangle consists of 90 + 45 + 45 = 180 degrees.

To find a missing angle in a triangle or a quadrilateral, add up the angles given and subtract from 180 degrees for a triangle and 360 degrees for a quadrilateral. Complementary angles-together two angles equal 90 degrees. Supplementary angles-together two angles equal 180 degrees. Use these relationships to find interior angles when given the exterior angle, or to find missing angles when given one angle.

Review triangle classifications by side length and by angle measure. Remind students angle measure corresponds to the opposite side length.

Student Practice

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8. If the measure of angle A in a parallelogram is 134 degrees, what is the measure of angle B?

9. What is the measure of angle X?

Student Practice Answers

1.

Students need to understand that quadrilaterals are 360 degrees so 110 + 110 = 220, 360-220=140. 140 divided between the remaining congruent angles is 70 degrees each. Angle 1 = 70 degrees 2.

A. is the correct answer. Supplementary is 180 degrees less the 70 listed=110

3.

The key word here is NOT complementary. The correct answer is A.

4.

G. is the correct answer. Two congruent sides makes the triangle isosceles, and the 104 degree angle makes it obtuse.

5.

J. is the correct answer. Base angles are at the bottom and the single hash marks correlate to the base angles and make them congruent, and visibly acute.

6.

F. is correct. Equilateral is all three sides are congruent. (Base word equal)

7.

B. is correct. Students need to find the missing angle to see it is obtuse. Angles given add up to 70 degrees subtracted from 180 degrees leaves the top angle 110 degrees.

8. If the measure of angle A in a parallelogram is 134 degrees, what is the measure of angle B?

Students need to understand to label the parallelogram from the top left corner and continue to label going clockwise. A parallelogram has two sets of parallel sides, so the top two angles are supplementary angles. 180-134=46 degrees

9. What is the measure of angle X?

Use the exterior angle of 59 degrees to see that together they form 180 degrees. X=121 degrees.