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3 years ago

Find the following angle measures. mEAD = ° mCAB = °

Mathematics

2 answers:

Dimas [21]3 years ago

8 0

29 and 119
Just did it :(

sergejj [24]3 years ago

6 0

<u>Part 1)</u> Find m∠EAD

we know that

m∠EAD+m∠DAF+m∠BAF= $180\°$ ----> by supplementary angles

solve for m∠EAD

m∠EAD= $180\°$ -(m∠DAF+m∠BAF)

in this problem we have

m∠DAF= $90\°$

m∠BAF= $61\°$

substitute in the formula above

m∠EAD= $180\°-90\°-61\°=29\°$

therefore

<u>the answer part 1) is </u>

m∠EAD= $29\°$

<u>Part 2)</u> Find m∠CAB

we know that

m∠CAB+m∠BAF= $180\°$ --------> by supplementary angles

solve for m∠CAB

m∠CAB= $180\°$ -m∠BAF

in this problem we have

m∠BAF= $61\°$

substitute in the formula above

m∠CAB= $180\°-61\°=119\°$

therefore

<u>the answer part 2) is</u>

m∠CAB= $119\°$

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<h2>Proportions</h2>

Proportions look like two fractions set equal to each other with a missing variable to solve.

<h3>State our variables</h3>

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<h3>Write a proportion</h3>

The first fraction has a number for the numerator (top) and denominator (bottom), because the question gives us the information. The second fraction has a missing value, <em>x</em>, that we are solving for. We can write <em>x</em> in the numerator.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}$

<h2>Solve</h2>

We can solve by finding the scale factor. The scale factor is the number we can multiply the numerator by to find <em>x</em>.

<h3>Find the scale factor</h3>

Start with the proportion.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}$

To find the scale factor,

Take the denominator from the fraction with a variable: $1\ hr$
Take the denominator from the fraction that has no variable: $\frac{1}{3}\ hr$
Divide step 1 by step 2 and solve: $1\ hr\ \div\ \frac{1}{3}\ hr = 3$

Our scale factor is <u>3</u>.

<h3>Solve for x</h3>

We can find <em>x</em> by multiplying the numerator in the first fraction by the scale factor. This is because <em>x</em> is also in the numerator.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{(\frac{1}{30}\ mi)*3}{1\ hr}}$