Given: AB ≅ BC , AE ≅ FC Prove: m∠AEC=m∠AFC

Answer:

EC/AB = FC/MA

Step-by-step explanation:

We are given AB

≅

BC that means that side AB and side BC are equal also we know that angle opposite to equalt

sides are equal.

Hence, ∠BAE=∠BCE-------(1)

Also ∠AEB=∠CEB.

Now we are given that: ∠ABC = 130°30’ i.e. in degrees it could be given as:

60'=1°

30'=(1/2)°=0.5°

Hence ∠ABC = 130°30’=130+0.5=130.5°

Also we know that sum of all the angles in a triangle is equal to 180°.

Hence,

∠BAE+∠BCE+∠ABC=180°.

2∠BAE+130.5=180 (using equation (1))

2∠BAE=49.5

∠BAE=24.75°  (DIVIDE BOTH SIDE BY 2)

Now in triangle ΔBEC  we have:

∠BEC=90° , ∠BCE=24.75°

SO,

∠BEC+∠BCE+∠EBC=180°.

Hence, 90+24.75+∠EBC=180

∠EBC=180-(90+24.75)

∠EBC=65.25°

Now we are given AE = 10 in

Also ∠BEA= 90°.

And ∠BAE=24.75°; hence using trignometric identity to find the measure of side BE.

\begin{gathered}\tan 24.75=\dfrac{BE}{AE}=\dfrac{BE}{10}\\\\BE=10\tan 24.75-------(2)\end{gathered}tan24.75=AEBE=10BEBE=10tan24.75−−−−−−−(2)

similarly in right angled triangle ΔBEC we have:

\begin{gathered}\tan 24.75=\dfrac{BE}{EC}\\\\\tan 24.75=\dfrac{BE}{EC}\\\\EC=\dfrac{BE}{\tan 24.75}------(3)\end{gathered}tan24.75=ECBEtan24.75=ECBEEC=tan24.75BE−−−−−−(3)

Hence, using equation (2) in equation (3) we get:

EC=10 \text{in.}EC=10in.

Hence AC=AE+EC=10+10=20 in.

Hence side AC=20 in.

Shelly buys a desk to sell in her shop. She marks the price up by 35% and sells the desk for $290.25. What price did Shelly pay for the desk? Please explain

I bet you $13456324567 dollars you didn't read that number. You just skipped right over it. You didn't realize I put a letter in it. No I didn't but you went back and looked.

An antelope can run at a speed of 61 miles per hour. What is this speed in yards per second? Round to the nearest hundredth. ​

Ajay is 5 cm taller than Aiden. If h represents Ajay's height, then Aiden's height is
expressed by:

Please help! I linked it to this question

Please help me on this IXL it's S.10 in Algebra.

(-4/5) X - 5 = -35
Can Someone solve for X

The questions are on the pictures ( I’m sorry that there are so much pictures but I couldn’t make the page smaller)

Tyler’s math class found that it would take 2.5×10^8 dollar bills to cover a square mile area. The surface area of the United States is about 3.8×10^6 square miles. About how many dollar bills are needed to cover the United States?
A)6.3×10^14


B)9.5×10^14


C)6.3×10^48


D)9.5×10^48

Solve
1. -6(2+x)
2. -9(-5-4c)
3. -1.4(-5+7g)
4. -4/3(3q-10)
5. -9(8+6n-4)
6. 2.3h(6-k)
7. 2(-2w-1.2+7x)
8. -2(h+8k)

Please and Thank You <3

which is the same as moving the decimal point 3 places to the left in a decimal number?

a. dividing the number by 1,000 b. Multiplying the number by 1,000

c. multiplying the number by 100 d. dividing the number by 100

What form is the equation below written in?

Luisa ate 3 ounces of pretzels.

The pretzels she ate contained
grams of protein.

Ples helpe me its math

Which of the following equation is true ?

4(b+1) ≤ 2(2b+1)+1
Is this equation no solution?
Very important

Mr. Shen likes for his homework assignments to have 2 addition problems for every 3 subtraction problems.

Which of the following homework assignments could Mr. Shen create?

A. 3 addition problems and 4 subtraction problems
B. 6 addition problems and 9 subtraction problems
C. 16 addition problems and 24 subtraction problems
D. 8 addition problems and 12 subtraction problems
E. 15 addition problems and 10 subtraction problems

Jake is working on different patterns found in his math journal. He begins evaluating the problems below: 0.236 x 101 = 2.36 0.236 x 102 = 23.6 0.236 x 103 = 236 By what power of 10 would Jake multiply 0.236 to get the product of 2,360,000?

If Cinderella shoe fit perfectly how come it fell off while she was running.

I give brainliest and 15 points plz help asap

Which is close to zero?
5/8, 9/18, 2/5, 10/11, 1/7

Would you times it by 4 since it’s 4 sides??

Help me find the slope Plz show steps i’m confused.

Which number below has a value between 6.6 and 6.7?




√6


√36


√44


√49

________ is measured in units of distance per unit of time.

Question 2 options:

Velocity


Speed


Force


Distance

(a) How could you calculate 23 x 4 on your calculator if the 4 button is broken? (b) How could you calculate 23 x 21 if the 2 button on your calculator is broken?

A school has 400 students. They all come to school by bus, and each bus carries the same number of students. How many students might there be on each bus?

I put some counters into groups with the same number in each group. I can’t remember what I did, but I do remember that I had 12 counters. What might the groups have been?

help mewa plzzzzzzzz

One thumbtack weighs 0.25 ounces. Once ounce is approximately equals to 28 grams. Which of the following is closet to the weight of one thumbtack in grams?

WHATS 1+1+ 6454873648768746832476387067367386378826846643737?

PLES HELP ME!!!!!!!!!!!!!!!!!!!! I NEED HELP ASAP