Download 4: The measure of the vertex angle of an isosceles triangle is given

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1 – 4: The measure of the vertex angle of an isosceles triangle is given.
Find the measure of a base angle.
1. 20
2. 90
3. 76
Geometry
Assignment #15
Angles of a Triangle
4. 110
5 – 8: The measure of a base angle of an isosceles triangle is given.
Find the measure of the vertex angle.
5. 80
6. 20
7. 45
8. 63
9 – 12: Use the diagram to the right.
9.
D
If m∠A = 40 and m∠B = 20 , find m∠ACD and m∠ACB .
C
10. If m∠A = 40 and m∠B = 50 , find m∠ACD and m∠ACB .
11. If m∠A = 40 and m∠ACB = 120 , find m∠ACD and m∠B .
12. If m∠A = 40 , m∠B = 3x + 20 , and m∠ACD = 5x + 10 ,find m∠B ,
m∠ACD , and m∠ACB .
A
13. In ΔABC , m∠A = 2x + 18 , m∠B = x + 40 , and m∠C = 3x − 40 .
a. Find the measure of each angle of the triangle.
b. Which is the longest side of the triangle?
14. The measure of an exterior angle at B, the vertex of isosceles ΔABC , can be represented
by 3x + 12. If the measure of a base angle is 2x – 2, find the measure of the exterior
angle and the measure of the interior angles of ΔABC .
R1. The accompanying diagram shows intersecting lines A
and m. Solve for the value of x.
R2. Two angles are complementary. One angle has a measure that is five times the measure
of the other angle. What is the measure, in degrees, of the larger angle?
HJJG
HJJG
R3. In the accompanying diagram, parallel lines AB and CD are
HJG
intersected by transversal EF at points X and Y, and
m ∠ FYD = 123. Find m ∠ AXY.
Island Trees Math Department
B
R4. Three sentences are written. The truth values are given for the first two sentences.
Determine whether the third sentence is true, false, or has an uncertain value.
Jon and Edith like to eat ice cream.
(False)
Jon likes to eat ice cream.
(True)
Edith likes to each ice cream.
(?)
R5. Identify the hypothesis and the conclusion for the following sentence:
“The perimeter of a square is 4s if the length of one side is s.”
R6. Write the sentence “Danny will change the tire if the car has a flat tire.” in symbolic form
using the symbols given:
Let p represent “The car has a flat tire.”
Let r represent “Danny will change the tire.”
R7. Write the inverse of the statement, “If it rains today, we will not have soccer practice.”
1. 80
2. 45
3. 52
4. 35
5. 20
6. 100
7. 90
8. 54
9. 60
10. 90
11. 60
12. 95, 135, 45
13. (a) 72, 67, 41 (b) BC
14. 30, 30, 120
R1.
R2.
R3.
R4.
R5.
x=8
75
57
F
H: The length of one side is s.
C: The perimeter of a square is 4s.
R6. p → r
R7. If it does not rain today, then
we will have soccer practice.
Island Trees Math Department