Mathematics: Given: m∠eyl=72° find: mehl , mlve

B. 400; 0/10;3 1 s; 0 1/10s; 8 1/100s...

Given: m∠eyl=72° find: mehl , mlve - id723943384, Xlhoncho45

Ответ:

doglover7963

10.01.2022

Mathematics

Part 1) The measure of arc EHL is $108\°$

Part 2) The measure of angle LVE is $54\°$

Step-by-step explanation:

step 1

Let

x-----> the measure of arc EHL

y----> the measure of arc EVL

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

we have

substitute

$72\°=\frac{1}{2}(y-x)$

$144\°=(y-x)$

$y=144\°+x$ ------> equation A

Remember that

$x+y=360\°$ -----> equation B ( complete circle)

substitute equation A in equation B and solve for x

$x+(144\°+x)=360\°$

$2x=360\°-144\°$

$x=216\°/2=108\°$

Find the value of y

$y=144\°+x$

$y=144\°+108\°=252\°$

therefore

The measure of arc EHL is $108\°$

The measure of arc EVL is $252\°$

step 2

Find the measure of angle LVE

we know that

The inscribed angle measures half that of the arc comprising

Let

x-----> the measure of arc EHL

we have

$x=108\°$

substitute

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Given: m∠eyl=72°
find: mehl , mlve

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