Question

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°

Answer 1

Answer:

$arc\ BEC=134^o$

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

$m\angle ABC=\frac{1}{2}(arc\ AC)$

substitute the given value

$75^o=\frac{1}{2}(arc\ AC)$

$arc\ AC=150^o$

step 2

Find the measure of arc BEC

we know that

$arc\ AB+arc| AC+arc\ BEC=360^o$ ---> by complete circle

substitute the given values

$76^o+150^o+arc\ BEC=360^o$

$arc\ BEC=360^o-226^o=134^o$

Answer 2

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

$<ACB=\frac{1}{2} arc(AB)\\<ACB=\frac{1}{2} (76)\\<ACB=38$

Sum of interior angles in a triangle is 180 degrees

$<A+<B+<C=180\\<A+38+75=180\\<A=180-38-75\\<A=67$

Now we find out arc BEC

<A = half of arc BEC

$67=\frac{1}{2} arcBEC\\67 \cdot 2= arc BEC\\134= arcBEC$

The measure of arc BEC is 134 degrees

Learn more :  brainly.com/question/20114323