Question

m∠uvz = 30° and m∠zvw = 78°. find m∠uvw
w
v
z
u
m∠uvw=
°
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Explanation:

Step1: Identify angle addition

To find \( m\angle UVW \), we use the angle addition postulate, which states that if two angles share a common side and vertex, the measure of the larger angle is the sum of the measures of the two smaller angles. Here, \( \angle UVW = \angle UVZ + \angle ZVW \).

Step2: Substitute the given values

We know \( m\angle UVZ = 30^\circ \) and \( m\angle ZVW = 78^\circ \). Substituting these into the equation:
\( m\angle UVW = 30^\circ + 78^\circ \)

Step3: Calculate the sum

Adding the two angles: \( 30 + 78 = 108 \), so \( m\angle UVW = 108^\circ \).

Answer:

\( 108 \)