Circle D is inscribed with triangle A B C. The measure of arc A B is 76 degrees. Point E is on the circle between points B and C. What is the measure of arc BEC in circle D? 134° 150 209° 210°

Circle D is inscribed with triangle A B C

The measure of arc BEC is 134 degrees

Given :

Circle D is inscribed with triangle A B C. The measure of arc A B is 76 degrees.

Inscribed angle is equal to half of intercepted arc

Sum of interior angles in a triangle is 180 degrees

Now we find out arc BEC

<A = half of arc BEC

The measure of arc BEC is 134 degrees

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Step-by-step explanation:

step 1

Find the measure of arc AC

we know that

The inscribed angle is half that of the arc it comprises

so

substitute the given value

step 2

Find the measure of arc BEC

we know that

---> by complete circle

substitute the given values

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there are two angles that are alternate interior angle with angle 9

the angle 15 and angle 7 are alternate interior angle with angle 9.

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answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,