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3 years ago

A quadrilateral has angles that measure 87° 69° in 104° what is the measurement of the fourth angle

2 answers:

8 0

A quadrilateral has angles that add up to 360° so x is the fourth angle in 87+69+104+x=360
260+x=360
x=100° is the fourth angle

Kay [80]3 years ago

6 0

The sum of a quadrilaterals angles is 360 degrees. You have three of the angles so just need to add those and subtract from 360. Answer is 360-260=100 degrees

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White raven [17]

Answer:

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.

$m$

we have

$m$

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

$m$

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