The measure of ∠ B is 78°.
What is inscribed angle?
An inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.
What is inscribed angle theorem?
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
According to the question
m ∠ A= 42º.
mAB = 120°
By inscribed angle theorem :
mAB = 2 m∠C
120° = 2 m∠C
m∠C = 60°
now,
according to the sum of angle of triangle
m ∠ B + m∠C + m ∠ A = 180°
m ∠ B +60° + 42º= 180°
m ∠ B = 78°
Hence, the measure of ∠ B is 78°.
To know more about inscribed angle theorem here:
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