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1 NAME:
DATE:
INTEGRATED ALGEBRA 1
MR. THOMPSON
LESSON 7.
TRIANGLES
HOMEWORK ASSIGNMENT #52: PAGES 267-271: # 2 - 32 EVENS
EXAMPLE I^ 1.
Find the measure of the third angle of a triangle if the measures of two of the angles are 72.6° and 84.2°.
Solution Subtract the sum of the known measures from 180: Answer (^) 23.2° 180 — (72.6 + 84.2) = 23.
EXAMPLE 2
In AABC, the measure of^ LB^ is twice the measure of^ LA,^ and the measure of LC is 3 times the measure of LA. Find the number of degrees in each angle of the triangle.
Solution Let x = the number of degrees in LA. Then Zr = the number of degrees in LB. Then 3x = the number of degrees in LC.
The sum of the measures of the angles of a triangle is 1800. x + Zr + 3x = 180 6x = 180 Answer mLA = 30, mLB = 60, m.G.0 = 90 x = 30 2x = 60 3x = 90
Check 60 90 30
+ 60 + 90 =^ 180V
EXAMPLE 3
In isosceles triangle (^) ABC, (^) the measure of vertex angle C is 30° more than the measure of each base angle. Find the number of degrees in each angle of the tri- angle.
Solution (^) Let x = (^) number of degrees in one base angle, (^) A. Then x = (^) number of degrees in the other base angle, (^) B, and (^) x + (^) 30 = number of degrees in the vertex angle, C.
The sum of the measures of the angles (^) of a triangle is 180°. x + x + x + 30 = 180 3x + 30 = 180 3x = 150 x = (^) 50 x + 30 = 80
Check (^) 50 + 50 + 80 = 180
Answer mLA = (^) 50, (^) mLB = (^) 50, mL.0 = 80
XEB
Writing About Mathematics
- Ayyarn said that if the sum of the measures of two angles of a triangle is equal to the mea- sure of the third angle, the triangle is a right triangle. Prove or disprove Ayyam's statement.
Developing Skills In 3-5, state, in each case, whether the angles with the given measures can be the three angles of the same triangle.
- 30°, 70°, 80° (^) 5. 30°,110°,40°
In 6-9, find, in each case, the measure of the third angle of the triangle if the measures of two angles are:
- Can a triangle have: a. two right angles? b. two obtuse angles? c. one right and one obtuse angle? Explain why or why not.
- The measure of the vertex angle of an isosceles triangle is 3 times the measure of each base angle. Find the number of degrees in each angle of the triangle.
- The measure of each of the congruent angles of an isosceles triangle is 6° less than the mea- sure of the vertex angle. Find the measure of each angle of the triangle.
- In AABC, mLA = x, m.LB = x+^ 45, and mL.0 = 3x —15.
a. Find the measures of the three angles. b. What kind of triangle is^ AABC?
- In a triangle, the measure of the second angle is 3 times the measure of the first angle, and the measure of the third angle is 5 times the measure of the first angle. Fuld the number of degrees in each angle of the triangle.
- In a triangle, the measure of the second angle is 30° more than the measure of the first angle, and the measure of the third angle is 45° more than the measure of the first angle. Fuld the number of degrees in each angle of the triangle.
- AEFB is a straight line,^ mLAEG =^ 130, and mLBFG 140. a. Find mLx, mLy, and m/..z. b. What kind of a triangle is^ AEFG?
- In AKLM,mLK^ = 2x, mLL = x + 30, mLM = 3x -30. a. Find the measures of the three angles of the triangle. b. What kind of a triangle^ is AKLM?
NAME:
DATE:
INTEGRATED ALGEBRA 1
MR. THOMPSON
HOMEWORK - LESSON 7.
TRIANGLES
HOMEWORK ASSIGNMENT # 52:^ PAGES 267-271: # 2 - 32 EVENS
EXE CI
Writing About Mathematics
- Janice said that if two angles of a triangle each measure 60 0, then the triangle is equilateral. Prove or disprove Janice's statement.
C"j
eloping Skills n 3-5, state, in each case, whether the angles with the given measures can be the three angles of the same triangle.
In 6-9, find, in each case, the measure of the third angle of the triangle if the measures of two angles are:
- 60°, 40° (^) 8. 54.5°, 82.3°
- What is the measure of each angle of an equiangular triangle?
- What is the sum of the measures of the two acute angles of a right friangle?
- In ARST,n1Z.R = 70 and mL T = 40. a. Find the measure of LS.
b. Name two sides in (^) ARST that are congruent.
d. What type of triangle is ARST?
c. Why are the two sides congruent?
e. Name the legs, base, base angles, and vertex angle of this triangle.
- Find the measure of each base angle of an isosceles triangle if the measure of the vertex angle is: a. 200^ b.^500 c.^ 76°^ d. 1000^ e.^ 65°
- The measure of each of the congruent angles of an isosceles triangle is 90 less than 4 times the vertex angle. Find the measure of each angle of the triangle.
- The measures of the three angles of (^) ADEF can be represented by (x + 30)°, 2x°, and (4x — 60)°. a. What is the measure of each angle? (^) b. What kind of triangle is (^) ADEF?
- In a triangle, the measure of the second angle is 4 times the measure of the first angle. The measure of the third angle is equal to the sum of the measures of the first two angles. Find the number of degrees in each angle of the triangle. What kind of triangle is it?
O. In a triangle, the measure of the second angle is 5° more than twice the measure of the first angle. The measure of the third angle is 35° less than 3 times the measure of the first angle. Find the number of degrees in each angle of the triangle.
- In ARST,mLR = x,mLS = x +^ 30, mL.T =^ x —^ 30.
a. Find the measures of the three angles of the triangle.
K What kind of a triangle is ARS7?
