Unit: Angle RelationshipsStudent Handout 3

Name Answer Key

Date

ANGLE SUM

INTERIOR ANGLES OF TRIANGLES

We know that the sum angles in any

triangle always equals 1800

• Use what you know about parallel lines cut by a transversal to help you

prove this fact about the angle surn of triangles to be true.

PROOF l: Line A is parallel to Line B. Prove that the sum of the interior angles in Triangle CDE is 1800.

c

620 350BD

FACT EXPLAIN

Ll and LD are alternate interior angus620

350

- 83 0

and must be congruent.

and ZE cre alternate Interior anglesand must be congruent.

L 1, L2 and z?) must cdd up to 180line.because they form a straight

Conclusion: The sum of the interior angles in a triangle is 180 0 , because...By proving that angle 2measures 83 0, we can check the total sum of the angles in the triangle: 83 + 62 + 35 = 180.

PROOF 2: Line C is parallel to Line D. Lines E and F are transversals.

FACT EXPLAIN

C The three angles form a straight

1800line which equals 180.

z-2 and z4 are alternate interiorangles and must be congruent.

zl and L5 are correspondingangles and must be congruent.

Conclusion: The sum of the interior angles in a triangle is 1800 because...and we can replace L2 with /-4, and Ll with L5, then 7.3 + z4 + /-5 = 180.

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Use what you know about angle relationships to answer the following questions.

I. Line C is parallel to Line D. What is the measure of /-5 if /-2 = 480 and L3 = 930. Explain howyou found your answer.

c48 0 L3

L4 48 0

We know that angle 2 and 4 are congruent

because they are alternate interior angles.

Angles 3, 4, cnd 5 must add uo to 180, 30angle 5 = 39 0

Use what you know about the sum of angles in a triangle to set up and solve an equation to find

the measure of each missing angle.

2. a. 13K -3 4.

6803x +

Equation: Equation: Equation:

4x —- 20

1

Iqx + 66= 180 8x -20= 1808x + ICC =

550 750 500

370 800

680 500350

5. In Triangle JKL, LK is 3 times the rneasure of a, and LI- is 8 times the measure of LJ. Find

the measure of each angle in Triangle JKL,

It's helpful for students to draw c picture:

150 450 1200

Summarize today's lesson:

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