(02.06 MC) Quadrilateral RSTU, diagonals SU and RT intersect at point V. RSTU is a parallelogram. If m∠TSV = 31° and m∠SVT = 126°, explain how you can find the measure of ∠URV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

m∠URV = 23°

Step-by-step explanation:

RSTU is a parallelogram   Given

SU and RT are diagonals

Therefore, SU bisect angle ∠TSR and RT bisects ∠SRU

m∠TSV = 31°  Given

m∠SVT = 126° Given

∴ m∠STV = 180° - (m∠TSV + m∠SVT) = 180° - (126° + 31°) = 23° (Sum of angles in a triangle ΔSVT = 180°)

m∠STV = 23° = m∠URV (Alternate angles of parallel lines RU and ST of parallelogram RSTU)

m∠URV = 23°

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

answer: f = 32.2m

step-by-step explanation: that is the answer