Question

In isosceles trapezoid ABCD, AD = BC. what is angle a + angle c?

Answer 1

Through B, draw a straight line parallel to AD which meets CD at E.

Now, since AB∥DE and AD∥BE,

∴ABED is a parallelogram.

Thus, ED=AB=18cm

As, BE∥AD and CD is a transversal,

∴∠BED=∠D=60°

(∵∠ABE=∠D)

Since, in an isosceles trapezium, the base angles are equal, ∠C=∠D=60°

In ΔBEC,∠BEC+∠ECD+∠CBE=180°

(Angle sum property of a triangle)

⇒60° +60° +∠CBE=180°

⇒120° +∠CBE=180°

⇒∠CBE=180° −120°

⇒∠CBE=60°

As the measure of ∠BEC=60°,∠ECB=60° and ∠CBE=60° ,ΔCBE is an equilateral triangle, Thus

∴CE=BC=12cm(BC=AD=12cm)

Now, CE+ED=12+18

⇒DC=30cm

Hope this'll help you.

Answer 2

Answer:

isoceles triangles are those whose any two sides are equal and similar to other triangle then the angle between these two sides will also be equal