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maxonik [38]
3 years ago
7

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third is 92° more tha

n the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle.
The measure of the first angle is ______
The measure of the second angle is _____
The measure of the third angle is _______
Mathematics
2 answers:
lesya692 [45]3 years ago
7 0

Answer:

The measure of first angle is 44°.

The measure of second angle is 22°.

The measure of third angle is 114°.

Step-by-step explanation:

First, you have to form expressions for the 3 angles. Let second angle be x :

First angle = (2x)°

Second angle = x°

Third angle = (92 + x)°

Next, you have to add up altogether as the total angles in a triangle is 180° :

2x + x + 92 + x = 180

4x + 92 = 180

4x = 180 - 92

4x = 88

x = 88 ÷ 4

x = 22°

Lastly, you have to substitute the x-value into the expressions :

First angle = 2(22) = 44°

Second angle = 22°

Third angle = 92 + 22 = 114°

zvonat [6]3 years ago
4 0

Answer:

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 68 more than the measure of the second angle. Use the face that the sum of the three measures of the three angels of a triangle is 180 degree to find the measure of each angle. a) the measure of the smallest angle. b) The measure of the second largest angle. c) the measure of the largest angle.

Step-by-step explanation:

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The operation * on the set Z of integers is defined by x*y = 3x + 2y - 1, x, y E Z. Find the value of x such that x*2=5​
Assoli18 [71]

Answer:

x = 2/3

Step-by-step explanation:

Let's unpack the equation x*2=5 from our definition of *:

x*2=3x+2(2)-1=5 (where x\in \mathbb{Z})

Now that we've got things defined in terms of familiar operations, we can simplify and solve for x:

3x+2(2)-1=5\\3x+4-1=5\\3x+3=5\\3x=2\\x=2/3

8 0
2 years ago
Help me jim! geometry homework
Maksim231197 [3]

Question 1

The angles 52 degrees match up. So if the sides are in proportion, then the triangles are similar.

Notice how 8/12 = 18/27 is a true equation. So the sides are in proportion to one another.

Therefore, the triangles <u>are similar</u>. I used the <u>SAS similarity theorem</u>.

================================================================

Question 2

Let's find the missing angle of the triangle on the right. For now, make that missing angle to be x.

Rule: For any triangle, the three angles always add up to 180

x+70+32 = 180

x+102 = 180

x = 180-102

x = 78

The missing angle of the triangle on the left is 78 degrees

Repeat for the other triangle as well

y+78+32 = 180

y+110 = 180

y = 180-110

y = 70

Both triangles have the angles 32, 70, 78 in whatever order you wish.

Since the angles match up like this, <u>the triangles are similar</u> because of the <u>AA Similarity theorem</u>

Technically, we only need 2 pairs of congruent angles at minimum. But having 3 congruent pairs doesn't hurt either.

================================================================

Question 3

We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, <u>the two triangles are similar</u>.

This time we use the <u>AA Similarity theorem</u>

================================================================

Question 4

Let's divide the longest side of the bottom triangle by the longest side of the triangle on top

48/32 = 1.5

Now let's divide the shortest sides of each triangle in the same order

36/24 = 1.5

Repeat for the middle-most sides

45/30 = 1.5

We get the same linear scale factor 1.5 each time. Therefore, <u>the triangles are similar</u> due to the <u>SSS Similarity theorem</u>

================================================================

Question 5

Any angle is equal to itself due to the <u>reflexive property</u>. So that will go for reason number 2.

Reason 3 is <u>SAS similarity</u> because we have the sides in proportion (statement 1) and the angles are congruent (statement 2).

3 0
2 years ago
A man has a mass of 120kg, he reduces his mass by 15%, how many kilograms is that​
Varvara68 [4.7K]

Answer:

your answer should be 102kg i could be wrong.

5 0
1 year ago
Read 2 more answers
PLEASE HELP THIS IS DUE TODAY!!
AnnyKZ [126]

while excluding 0, the product and quotient is positive if operating between same sign, otherwise if we operating different sign will resulted negative.

7 0
3 years ago
Need now for study guide
likoan [24]

Answer:

17 cm.

Step-by-step explanation:

Because 12 cm + 5 cm. is 17  cm.

8 0
3 years ago
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