Given: circle k(O), m∠A=(x+45)°, m KE =(x+20)°, m EW =(3x)° Find: m KW . HELP ASAP WILL GIVE BRAINLIEST!

We can use the central angle theorem for this. It says that an angle inscribed in a circle (on the circumference) measured half of the arc it intercepts (by 2 points on the circumference of the circle).

that would mean that Angle KAW is half of measure of Arc KW. Thus we can write:

m∠A = 0.5 (arc KE + arc EW)

x+45 =0.5 (x+20+3x)

x+45 = 0.5(4x+20)

x+45 = 2x + 10

45 - 10 = 2x - x

Thus, x = 35

Since Arc KW = Arc KE + Arc EW and x = 35, we can say:

Arc KW = x + 20 + 3x = 35 + 20 + 3(35) = 160°

raphealnwobi raphealnwobi · Answer 2 · 2022-04-01T11:58:38+02:00

The value of the arc KW subtended from the center of circle O is 160°.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

From the circle O:

m KW = m KE + m EW (angle addition postulate)

m KW = (x + 20) + (3x)

m KW = 4x + 20

m KW = 2m∠A (angle subtended from center)

4x + 20 = 2(x + 45)

x = 35

m KW = 4(35) + 20 = 160°

The value of the arc KW subtended from the center of circle O is 160°.

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