Question

Find the value of x.

Answer 1

Answer:

The measure of angle x is 40°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs which comprises

see the attached figure with letters to better understand the problem

so

m∠x=(1/2)[arc AB-arc AC]

Find the measure of arc AC

we know that

arc AB+arc BC+arc AC=360° ----> by complete circle

substitute the given values

arc AB=200°

arc BC=40°

arc AC=?

200°+40°+arc AC=360°

240°+arc AC=360°

arc AC=360°-240°=120°

Find the measure of angle x

m∠x=(1/2)[200°-120°]=40°