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cricket20 [7]
3 years ago
9

I NEED HELP PLEASE ! :)

Mathematics
1 answer:
defon3 years ago
7 0

A theorem called "inscribed angle theorem," states that angle θ is half of that of angle 2θ that subtends an identical arc on the circle.

So, ∠ABC = center angle * 1/2

The center angle is 192°, so substitute with that number and solve.

∠ABC = 192 * 1/2

∠ABC = 96°

Therefore, the answer is 96°

Best of Luck!

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In trapezoid ABCD, AC is a diagonal and ∠ABC≅∠ACD. Find AC if the lengths of the bases BC and AD are 12m and 27m respectively.
xz_007 [3.2K]

Answer:

Length of diagonal is 18 m

Step-by-step explanation:

Given in trapezoid ABCD. AC is a diagonal and ∠ABC≅∠ACD. The lengths of the bases BC and AD are 12m and 27m. We have to find the length of AC.

Let the length of diagonal be x m

In ΔABC and ΔACD

∠ABC=∠ACD      (∵Given)

∠ACB=∠CAD      (∵Alternate angles)

By AA similarity theorem, ΔABC~ΔACD

∴ their corresponding sides are proportional

\frac{x}{27}=\frac{12}{x}=\frac{AB}{CD}

Comparing first two, we get

⇒ \frac{x}{27}=\frac{12}{x}

⇒ x^2=27\times 12

⇒ x=\sqrt324=18

hence, the length of diagonal is 18 m



4 0
3 years ago
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Semmy [17]

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3 0
2 years ago
Solve for x.<br><br><br><br> Enter your answer in the box.<br><br> x =____°
Vlad1618 [11]

we know that

The sum of all interior angles in the polygon is equal to the formula

(n-2)*180\°

where

n is the number of sides of the polygon

In this problem we have

n=6

substitute the value in the formula

(6-2)*180\°=720\°

<u>Find the value of x</u>

720\°=x\°+108\°+113\°+132\°+75\°+160\°\\720\°=x\°+588\°\\x\°=720\°-588\°\\x=132\°

therefore

<u>the answer is</u>

the measure of x is 132\°


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