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loris [4]
3 years ago
10

ZA and ZB are complementary angles. If m A = (x – 21)° and m

Mathematics
2 answers:
pogonyaev3 years ago
7 0

Answer:

A = 21

Step-by-step explanation:

Complementary angles add to 90

x-21 + 2x-15 = 90

Combine like terms

3x -36 = 90

3x-36+36 = 90+36

3x = 126

Divide by 3

3x/3 =126/3

x = 42

We want to find ZA = x-21

A = 42-21

A = 21

Lelu [443]3 years ago
4 0

If the sum of the measures of two angles is 90° they are known as complementary angles.

<h3 /><h3>According to the question</h3>

\bf \large \longrightarrow \:  \:( x \:  -  \: 21) \:  +  \: (2x \:  -  \: 15) \:  =  \: 90 \degree

Now , Opening brackets and simplifying

\bf \large \longrightarrow \:  \: x \:  -  \: 21 \:  +  \: 2x \:  -  \: 15\:  =  \: 90 \degree

\bf \large \longrightarrow \:  \:3x \:  -  \: 36 \:  =  \: 90 \degree

\bf \large \longrightarrow \:  \:3x \:  =  \: 90 \: +  \: 36

\bf \large \longrightarrow \:  \:3x \:  =  \: 126

\bf \large \longrightarrow \:  \:x \:  =  \:  \frac{126}{3}  \\

\bf \large \longrightarrow \:  \:x \:  =  \:   \cancel\frac{126}{3}   \: \:  \large \: ^{42}  \\

\bf \large \longrightarrow \:  \: x \:  =  \: 42

Now , we have to find ZA .

  • ZA = x - 21

\bf \large \implies \:  \:A \:  =  \: 42 \:  -  \: 21

\bf \large \implies \:  \:A \:  =    \: 21

The measure of angle ZA is 21°

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Two angles of a triangle have the same measure and the third one is 18 degrees greater than the measure of each of the other two
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Answer:

72°

Step-by-step explanation:

Let the 2 equal angles be x then the third angle is x + 18

The sum of the 3 angles in a triangle = 180°, thus

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3x + 18 = 180 ( subtract 18 from both sides )

3x = 162 ( divide both sides by 3 )

x = 54

Hence

the largest angle = x + 18 = 54 + 18 = 72°

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Mandarinka [93]

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Where will her cut be located? Round to the nearest tenth. x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 A
Arte-miy333 [17]

Answer:

The correct answer is 25.2 in.

Step-by-step explanation:

It is given that number line goes from 0 to 60 which can be used to represent a ribbon of length = 60 inches.

2 inches of the ribbon are frayed so actual length = 58 inches

Please refer to the attached image for the ribbon.

A is at 0

C is at 60

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P is the point to divide the remaining ribbon in the ratio 2:3.

Part AB of the ribbon is frayed.

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Let BP = 2x and PC = 3x

Now, BP + PC = BC = 58 = 2x + 3x = 5x

So,

5x =58\\\Rightarrow x =11.6

BP = 2\times x = 2 \times 11.6 = 23.2\ inches

Location of the Cut = 2 + 23.2 = <em>25.2 inches</em>

<em></em>

Alternatively, we can use the formula directly:

x = \dfrac{m} {m + n } (x_2 - x_1) + x_1

x_1 = 2\\x_2 = 60

m: n is the ratio 2:3

x = \dfrac{2} {2 +3 } (60- 2) + 2\\\Rightarrow 0.4 (58 )+2\\\Rightarrow 23.2+2 \\\Rightarrow \bold{25.2\ inches}

5 0
3 years ago
Read 2 more answers
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