1. ABCD is a kite. Find 𝑚∠𝐴, 𝑚∠𝐶, 𝑎𝑛𝑑 𝑚∠𝐷.

Question

1. ABCD is a kite. Find 𝑚∠𝐴, 𝑚∠𝐶, 𝑎𝑛𝑑 𝑚∠𝐷.

m-angle-A = (x+20)

m-angle-B= 140

Answer 1

I would recommend writing down what you know first.

1. We know that all the angles in a quadrilateral add to 360°
2. Angle A= (X+20°)
3. Angle B = 140°

Since the triangle should be drawn in the order of ABCD, I will put A at the "top" of the kite, B on the right side, C at the bottom and D on the left side (opposite B).

1. We know based on the description of the kite above, that Angle B = Angle D, so:
2. Angle B = 140°

We are left with solving for Angle A and Angle C (which we will call X), now we have this equation:

1. A + B + C + D = 360°
2. (X+20°) + 140° + X + 140° = 360° gather like terms and solve for X
3. 2X + 300° = 360°
4. 2X = 60°
5. X = 30°
6. A = 50°, B = 140°, C = 30°, D = 140°