Question

Quadrilateral UVWX is a rhombus and m∠TVU=a+24°. What is the value of a?

Answer 1

Answer:

9

Step-by-step explanation:

<utv=<utx=90°

x u t=57°

so<txu =33°

triangle xtu and uty are congruent

so <txu=<tvu

33=24+a

a=9°

Answer 2

Answer:

Quadrilateral UVWX is a rhombus and m∠TVU=a+24°. What is the value of a?

Answer : a = 9

Step-by-step explanation:

A rhombus is a type of parallelogram, and what distinguishes its shape is that all four of its sides are congruent.

All 4 sides are congruent (equal).

Diagonals are perpendicular (90°).

∠UTV = ∠UTX=90°   [Since diagonals intersect at 90°]

In figure, given that

∠XUT = 57°

Hence

∠TXU =33°

Triangle ΔXTU and ΔUTY are identical.

therefore,

∠TXU = ∠TVU

⇒ 33° = 24° + a

⇒ a=9°

Therefore, the value of a will be 9°.