2. Given that 𝑚∠𝐴=3𝑥+5𝑦, 𝑚∠𝐵=𝑥−𝑦+20,𝑚∠𝐶=4𝑥+3𝑦+16. Find the measure of each angle of square ABCD. Round to 1 decimal place.

Answer 1

Interesting question: Since ABCD is a square, the each angle is a right angle and 90°.

I assume you are looking to solve x and y. If so, solve following system equations to get x and y

3𝑥+5𝑦=90

𝑥−𝑦+20=90

substitution: 3(y+70) + 5y = 90 > y=-15, x=55,

The answers will not apply to angle <C: 4𝑥+3𝑦+16=90.

Therefore, ABCD could not be a square.

If ABCD is quadrilateral polygon, then the sum of the interior angle equals 360° ,

3𝑥+5𝑦+𝑥−𝑦+20+4𝑥+3𝑦+16=360

without any more information, we cannot resolve x and y value.

Answer 2

All angles of a square are equal.

Can you use this fact to solve?