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TUESDAY 1. An escalator in a shopping mall is 40 ft long and 32 ft tall. To the nearest hundredth, what distance does the escalator carry shoppers? 2. The measures of three angles of a triangle are given by (8x - 5)°, (2x)°, and (3x - 10)°. What is the measure of the largest angle? 3. Gina is traveling from Statesboro to Guyton. Gina plans to drive to Guyton using Golf Rd. and Soccer Ln. Golf Rd. is 8 miles long and Soccer Ln. is 6 miles long. How many fewer miles would Gina have traveled if she would have taken a boat instead? 40²+ 32² = c² = c c² = 2,624 c = feet (8x - 5)° +(2x)° + (3x - 10)° = x – 15 = x = 195 x = 15 8(15) - 5 = 115˚ 6²+ 8² = c² 100 = c² 10 = c 14 miles – 10 miles = 4 miles less
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1. Please have out your
HOMEWORK to be stamped.2. Please work through the next 3
sections of your Skill Builder. 3. TURN in TRANSVERSALS PAGE
to the box.
TUESDAY1. An escalator in a shopping mall is 40 ft long and 32 ft tall. To the nearest hundredth, what distance does the escalator carry shoppers?
2. The measures of three angles of a triangle are given by (8x - 5)°, (2x)°, and (3x - 10)°. What is the measure of the largest angle?
3. Gina is traveling from Statesboro to Guyton. Gina plans to drive to Guyton using Golf Rd. and Soccer Ln. Golf Rd. is 8 miles long and Soccer Ln. is 6 miles long. How many fewer miles would Gina have traveled if she would have taken a boat instead?
40²+ 32² = c²
1600 + 1024 = c
c² = 2,624 c = 51.22 feet
(8x - 5)° +(2x)° + (3x - 10)° = 180
13x – 15 = 180
13x = 195x = 158(15) - 5 =
115˚
6²+ 8² = c²
100 = c²
10 = c
14 miles – 10 miles =
4 miles less
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180o.
32
1
m<1 + m<2 + m<3 = 180°
*
Ex: 1What is the missing angle?
70º70ºx+
180º70º
x
180 – 140 = 40˚
*
45x 10x
35x
Find all the angle measures
180 = 35x + 45x + 10x180 = 90x 2 = x
* 70˚
90˚ 20˚
What can we find out?
The ladder is leaning on the ground at a 65º angle. At what angle is the top of the ladder touching the building?
180 = 65 + 90 + x180 = 155 + x
25˚ = x
*
Extention to Triangle Sum Theorem
The acute angles of a right triangle are complementary.
m A + m B = 90∠ ∠ o
*
The tiled staircase shown below forms a right triangle.The measure of one acute angle in the triangle is twice the
measure of the other angle. Find the measure of each acute angle.
Find the missing angles.
2x + x = 90˚3x = 90˚
x = 30˚
30
60
Find the missing angles.
2x + (x – 6) = 90˚3x – 6 = 903x = 96 x = 32
2(32) = 64˚
32 – 6 = 26˚
*
64
2
Example: Find x and the measure of each angle.
C
(𝟗 𝒙−𝟒)𝟎x =
m<A=
m<B=
m<C=
A
B
(𝟖𝟔)𝟎
(𝟕𝒙+𝟐)𝟎
*6
50 ˚
44 ˚
86 ˚
TRIANGLE SUM THEOREM
This packet is due Thursday. Please complete # 1-16 tonight for homework as well as your
Weekly Homework.
