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In the circle below, suppose 
mVUX^(⏜)=156^(@) and 
m/_UVW=79^(@). Find the following.
(a) 
m/_VUX= 
◻ 。
(b) 
m/_UXW= 
◻ 。

In the circle below, suppose m \overparen{V U X}=156^{\circ} and mUVW=79 m \angle U V W=79^{\circ} . Find the following.\newline(a) mVUX= m \angle V U X= \square \newline(b) mUXW= m \angle U X W= \square

Full solution

Q. In the circle below, suppose m \overparen{V U X}=156^{\circ} and mUVW=79 m \angle U V W=79^{\circ} . Find the following.\newline(a) mVUX= m \angle V U X= \square \newline(b) mUXW= m \angle U X W= \square
  1. Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of its intercepted arc.\newlinem/VUX=12×mVUX()m/_{VUX} = \frac{1}{2} \times mVUX^{(\bigcirc)}\newlineCalculation: 12×156=78\frac{1}{2} \times 156 = 78
  2. Calculation for Inscribed Angle: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.\newlinem/UXW=m/UVW+m/VUXm/_{UXW} = m/_{UVW} + m/_{VUX}\newlineCalculation: 79+78=15779 + 78 = 157

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