DC = 10 what is the value of AB and what is the measure of angle ABD

Question

It is a rectangle made of up two right triangles. Between D and C it is 60 degrees

example:

A. B

D. 60 C

the options for the first question are

10sqr 3 , 10 sqr 2 , 20, 10

Answer 1

I'm assuming this is the picture you are describing:

If so, in a rectangle, opposite sides are congruent so segment AB ≅ segment DC, therefore segment AB = 10.

Also, segment AD ≅ segment AD (by the Reflexive property), m∠ADC = 90° and m∠ABC = 90° therefore ΔADC ≅ ΔDAB (by SAS ≅). Because the triangles are congruent, the corresponding angles are congruent therefore ∠DCA ≅ ∠ABD = 60°