Answer:
<em>160°</em>
<em />
Step-by-step explanation:
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).
<em>that would mean that Angle KAW is </em><em>half </em><em>of measure of Arc KW.</em> 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
<em>Since Arc KW = Arc KE + Arc EW and x = 35, we can say:</em>
<em>Arc KW = x + 20 + 3x = 35 + 20 + 3(35) = 160°</em>
Answer:
d. m<ABD = 50°, m<GBC = 47°, m<EBC = 50°, and m<DBG = 83°
Step-by-step explanation:
m<ABF = 47° (given)
m<FBE = 83°
✍️m<ABD + m<ABF + m<FBE = 180° (angles on straight line)
m<ABD + 47° + 83° = 180° (substitution)
m<ABD + 130° = 180°
Subtract 130 from each side
m<ABD = 180° - 130°
✅m<ABD = 50°
✍️m<GBC = m<ABF (vertical angles)
✅m<GBC = 47° (Substitution)
✍️m<EBC = m<ABD (Vertical angles)
✅m<EBC = 50° (substitution)
✍️m<DBG = m<FBE (vertical angles)
✅m<DBG = 83° (Substitution)
