Question

What is angle a?

Answer 1

128.5°

Explanation:

Because the length of side AB is equal to the length of side CB, and the length of side AD is equal to the length of DC we know it is a kite (length congruence given). You can approach the problem by splitting the kite into two congruent triangles, the dashed line represents how the kite is split (The angles B and D are bisected, AB = CB, so they are congruent by AAS). Because `angle B` is bisected, `angle DAB` is just `(angle B )/ 2`, which is `95/2=47.5°`. You can use the same process to find `angle ADB`, with `8/2=4°`.

`angleDAB + angle ADB + angle BDA = 180°` (Sum of interior angles of a triangle are 180°). Therefore, `angle DAB = 180° -angle ADB - angle BDA = 180° - 47.5° - 4° = 128.5°`

Hope this helps!