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 wo

Question

3 years ago

12

rk, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

2 answers:

Tomtit [17] · Answer 1 · 2022-10-02T09:38:06+03:00

5 0

Answer:

78 degrees

Step-by-step explanation:

const2013 [10] · Answer 2 · 2022-10-02T07:21:06+03:00

Opposite angles in a parallelogram have equal measure.

The measure of angle TUV is 78 degrees

The given parameters are:

$\mathbf{\angle SRV = 48}$

$\mathbf{\angle SVR = 54}$

Start by calculating angle RSV.

$\mathbf{\angle RSV + \angle SVR + \angle SRV = 180}$ --- angles in a triangle

So, we have:

$\mathbf{\angle RSV + 54 + 48= 180}$

$\mathbf{\angle RSV + 102= 180}$

Subtract 102 from both sides

$\mathbf{\angle RSV = 78}$

Angles RSV and TUV are corresponding angles.

So, we have:

$\mathbf{\angle TUV = \angle RSV = 78}$

Rewrite as:

$\mathbf{\angle TUV = 78}$

Hence, the measure of angle TUV is 78 degrees