What is the angle of a?

[green ocean]

The two tick marks on AB and AE mean that they're the same length. So what kind of triange is BAE?

[median hawk]

bae is an isosceles triangle cuz 2 sides are equal

angle aeb= angle abe cuz they're base angles of an isosceles triangles

this means angle bae = 180-30-30=120
cuz of the angle sum property of triangles

im assuming abcd is a parallelogram and that angle bce =90

so angle bcd= angle bae=120
angle ecd or a=angle bcd-anglebce= 120-90=30

[azure fox]

∠AEB=30° due to isosceles, therefore ∠A=180°-2*30°=120°. ∠A=∠C and ∠B=∠D, assuming the question provided AB∥CD and AD∥BC. Assuming the question also provided ∠AEC=90° (or else there'd be infinite solves, for you are able to move point E to anywhere on AD), ∠BEC=90°-30°=60°

Due to corresponding interior angles (intercept on parallel), ∠BCE=90°

interior angle sum of a quadrilateral is 360°, for you may slice any quadrilateral into two triangles by a diagonal, so that all their angles composes into the angles of the quadrilateral

BAEC is a quadrilateral, therefore ∠B=360°-120°-90°-90°=60°

∠B=∠D, therefore ∠D=60°

inner angle sum of triangles, 180°-90°-60°=30°

aka 1/3 of a right angle

[azure fox]

.

[summer moss]

so

if you draw an imaginary line

inside the double angle

you get

a+30

as

both are alernate

and we know that angle EBC = 30 (CO interior) Therefore to find a we have the equation. a+30+30=a-120 (Angle BCE=120-a)

-2a=-60

a=30

degrees