Question

In a parallelogram ABCD, <B=2<C. What is the degree measure of <B and <C?​

Answer 1

Step-by-step explanation:

In any parellelogram ABCD, there are two facts that are always true:

The sum of the angles is always 360° (true for all convex quadrilaterals)

∠A=∠C , and ∠B=∠D

By corollary this means that 2B+2C=360°; B+C=180°. This property is what makes the opposite sides of a parellelogram parallel, as any polygon with two consecutive angles adding to 180° will have two parallel sides.

If B=C that gives us:

B+C=2B=180°

B=90°

And so if you have a parallelogram with two consecutive angles equal, you have a rectangle