Question

How do I find the missing measurements?

Answer 1

CD = 10

AD = 22

EC = 13

AC = 26

∠CAD = 23°

∠BAC = 47°

∠ADC =110°

Explanation:

A parallelogram is a quadrilateral with two sets of opposite parallel lines.

Which mean in ABCD parallelogram given AB is parallel to DC and BC is parallel to AD.

Now lets find the values required,

CD = AB (Opposite sides are equal in length)

But, AB= 10 (given) therefore CD = 10.

AD = BC (Opposite sides are equal in length)

But, BC= 22 (given) therefore AD = 22.

EC = AE (Diagonals bisect each other)

But, AE= 13 (given) therefore EC = 13

AC = AE + EC

=
`13+13`

AC =
`26`

∠CAD = ∠BCA (Alternate interior angles are equal)

But, ∠BCA = 23° therefore, ∠CAD = 23°

∠BAC = ∠ACD (Alternate interior angles are equal)

But, ∠ACD = 47° therefore, ∠BAC = 47°

∠ADC + ∠BCD = 180° (Consecutive interior angles)

But, ∠BCD = 23°+47°=70°

∠ADC = 180°- ∠BCD

=180°-70°

∠ADC =110°