Answer:
m∠QTP = 43°
Step-by-step explanation:
As with any problem, you start by looking at what you are given and the relationships between those things and what you are to find.
There are several relationships you can make use of here:
- the sum of angles of a triangle is 180°
- vertical angles are congruent
- corresponding angles are congruent where a transversal crosses parallel lines
The angles marked (3x°) and (5x-32)° are corresponding angles, so are congruent. That means you can find their measure:
3x = 5x -32
0 = 2x -32 . . . . . subtract 3x
0 = x -16 . . . . . . . divide by 2
16 = x . . . . . . . . . .add 16
3x° = 48° . . . . . . find 3x°
Angle TPQ is vertical with 3x°, so also has measure 48°. Angle TQP is vertical with the angle marked 89°, so also has measure 89°.
Now, you know two of the three angles in triangle QTP, so you can find angle QTP:
m∠QTP + 48° + 89° = 180° . . . sum of angles in a triangle
m∠QTP = 43° . . . . . . . . . . . . . . subtract 137°
There are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
<h3>What is the ratio?</h3>
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Combine ratio dogs:ferrets:cats = 5:1:9
Let's suppose the number of ferrets is x then:
5x + x + 9x = 45
15x = 45
x = 3
Ferrets x = 3
Dogs = 5x = 5(3) = 15
Cats = 9x = 9(3) = 27
Thus, there are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Learn more about the ratio here:
brainly.com/question/13419413
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First, find the scale factor.
8.4 / 7 = 1.2
9 / 7.5 = 1.2
7.2 / 6 = 1.2
Since both solids are different sizes, the solids aren't congruent.
The size ratio for all the sides are:
8.4:7
9:7.5
7.2:6
Since the scale factor isn't 1:1 this also proves that the solids are NOT congruent.
Since both solids are the same kind of shape and have an identical scale factor, the solids are similar.
Best of Luck!
Distance = speed rate x time
Speed rate = 120 miles per hour
Time = 3 hours
Replacing:
D = 120 mph x 3 h = 360 miles
Using the supplementary angles theorem, it is found that the measure of the second angle is of m<2 = 45º.
<h3>What are supplementary angles?</h3>
Two angles are supplementary when the <u>sum of their measures is of 180º</u>.
The Alabama state flag has <u>two lines opposite by the same vertex</u>, hence two angles that are sided are supplementary, hence:
m<1 + m<2 = 180º.
135º + m<2 = 180º.
m<2 = 45º.
The measure of the second angle is of m<2 = 45º.
More can be learned about supplementary angles at brainly.com/question/12919120
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