Quadrilateral RSTU, diagonals SU and RT intersect at point V.

RSTU is a parallelogram. If m∠TUV = 78° and m∠TVU = 54°, explain how you can find the measure of ∠SRV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

Question

Quadrilateral RSTU, diagonals SU and RT intersect at point V.

RSTU is a parallelogram. If m∠TUV = 78° and m∠TVU = 54°, explain how you can find the measure of ∠SRV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

Phantomdex · Answer

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AZ · Answer

Do you know what the sum of angles in a triangle is?

Phantomdex · Answer

Um well, I have no clue what's going on in this question. I don't know what to do on it at all nor how to solve it.

AZ · Answer

In a triangle, what do all the angles add up to?

Phantomdex · Answer

Shouldn't they add up to a degree of 180?

AZ · Answer

Yes! Can you find the third angle in the triangle now?

Phantomdex · Answer

Is it 45?

AZ · Answer

How did you get that?

AZ · Answer

All three angles should add up to 180.

x + 54 + 78 = 180

x = ??

Phantomdex · Answer

Yes, so shouldn't x = 45 because 54 and 78 give us 132 and if you add 45 that equals up to 180

Phantomdex · Answer

If I'm doing it correctly that is

AZ · Answer

No

132 + 45 = 177

AZ · Answer

To find the value faster, you can just do

180 - 132 = ?

Phantomdex · Answer

Oh, right I completely forgot about that method

Phantomdex · Answer

Is it 48 then?

AZ · Answer

Now that you found the angle of VTU, let's find the value of angle SRV

Do you know the alternate interior angle theorem?

Phantomdex · Answer

Isn't that when two parallel lines are cut by  transversal?

AZ · Answer

Essentially, the alternate interior angle theorem says that angle VTU and SRV are congruent because the two parallel sides are cut by a transversal line. Thus, the alternate interior angles are equal to each other

AZ · Answer

You got it!

Phantomdex · Answer

Oh, nice!

Phantomdex · Answer

So, what about SRV?

AZ · Answer

It is equal to angle VTU which we calculated as 48 degrees

Phantomdex · Answer

Yes, but I need to be able to explain how I've found the measure of SRV. Also needing to show my work. Unless we've done that already.

AZ · Answer

We've done it all in two steps

Phantomdex · Answer

Oh, then I apologize for being difficult.

AZ · Answer

1) You used the sum of all angles in a triangle is 180
2) You used the alternate interior angles theorem

AZ · Answer

@phantomdex wrote:

Oh, then I apologize for being difficult.

No worries! Geometry proofs can be a hassle

Phantomdex · Answer

Indeed

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