Question

9. Given that AB // CD, find the values of the unknowns
in each of the following figures....quick answer please​

Answer 1

Step-by-step explanation:

given ab║cd

∠ABC = ∠BCD = 37°

now, in ΔABC

∠A +∠B + ∠C =180°   (angle sum property of a triangle)

∴108 + 37 + ∠a = 180

∠a = 180 - 145

∠a = 35°

for ∠b

in Δ BCD, using exterior angle property

∠CBD + ∠BCD = ∠BDE

71 + 37 = ∠b

∠b = 118°

Answer 2

Answer:

a°= 35°  

b° = 108°

Step-by-step explanation:

Given that AB//CD in the figure.

To find the ∠a  and ∠b in the figure.

So,

From the given figure,

triangle ΔBCD, ∠CBD = 71° , ∠BCD= 37° and ∠BDE = b° is exterior angle.

Then , ∠CBD + ∠BCD = ∠BDE (by using exterior angle property)

               71° + 37°  =  b°

                  108°  =  b°

                   b°  = 108°

Again from the given figure,

∠BAC = 108°  and ∠ACD = ( a° + 37° )

∠BAC + ∠ACD = 180°  ( alternate interior angle)

108° + ( a° + 37° ) = 180°

108° + a° + 37° = 180°

a° + 145° = 180°

a° = 180° - 145°

a° = 35°

Therefore, a°= 35° and b° = 108°.

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