ABCD is a parallelogram. given that m<B=(5x-8)deg and m<D=(3x+14)deg, find m<B and m<C

Answer 1

Hi Karly,

ABCD is a parallelogram. given that m<B=(5x-8)deg and m<D=(3x+14)deg, find m<B and m<C

Given:

1. Parallelogram ABCD
2. m<B=(5x-8)deg
3. m<D=(3x+14)deg

Find: m angle B and C

To solve this you need to know the properties of a parallelogram

1. Opposite Sides are parallel and congruent
2. Opposite angles are equal, adjacent angles are supplementary
3. Diagonals bisect each other

We will use the property Opposite angles are equal and adjacent angles are supplementary to solve this problem.

In parallelogram ABCD, B and D are opposite angles. so they are equal.

m<B=(5x-8)deg = m<D=(3x+14)deg

5x-8 = 3x+14

2x = 22

x = 11

m angle B is

(5x-8)

(5 (11) - 8)

= 47

m angle D is same as B, but lets check the math to make sure we didn't make a mistake

3x+14

3(11) + 14

=47

So the measure of B and D is 47 Degrees

Now we will use the property of adjacent angles being supplementary

angle B + and C = 180 degrees

47 + C = 180

C= 133 degrees

So B = D = 47 degrees, and C = 133 Degrees

Hope this helps :)