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neariah24
13.06.2020 •
Mathematics
What is Bassima’s error
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Ответ:
69e.) 170
69d.) 140
Step-by-step explanation:
69e.)
This is a case of two secants that intersect inside a circle.
Segments IK and PV are secants that intersect inside circle O.
m<PSK = (1/2)(m(arc)PK + m(arc)IV)
m<VSK + m<PSK = 180
m<VSK = 38
m<PSK = 180 - 38
m<PSK = 142
142 = (1/2)(m(arc)PK + 114)
284 = m(arc)PK + 114
m(ark)PK = 170
69d.)
Let m(arc)PKV = x
Then m(arc)PIV = 7/2(m(arc)PKV) = 3.5x
A full circle has an arc angle measure of 360.
x + 3.5x = 360
4.5x = 360
x = 80
m(arc)PKV = 80
The measure of an angle with vertex on a circle formed by the intersection of a tangent and a chord is half the measure of the intercepted arc.
m<VPL = (1/2)m(arc)PKV
m<VPL = (1/2)(80)
m<VPL = 40
Angles VPL and VPJ are supplementary, so the sum of their measures equals 180 deg.
m<VPL + m<VPJ = 180
m<VPJ = 180 - m<VPL
m<VPJ = 180 - 40
m<VPJ = 140