Question

RSTU is a parallelogram. If m∠SRV = 48° and m∠SVR = 54°, explain how you can find the measure of ∠TUV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer: ∠TUV = 78°

Step-by-step explanation: The parallelogram is represented below, which shows the position of the given angles.

In a parallelogram, opposite angles are always the same, so:

m∠SRV = m∠VTU

Vertical angles angles are equal, so:

m∠RVS = m∠TVU

The sum of internal angles of a triangle is 180. Then, ∠TUV is:

m∠VTU + m∠TVU + m∠TUV =180

48 + 54 + x = 180

102 + x = 180

x = 180 - 102

x = 78

Angle m∠TUV equals 78°.