Mm< b = 80 + x
m< c=110 - 3x
m quadrilateral abcd is a parallelogram if both pairs of opposite angles are equal. prove that quadrilateral abcd is
a parallelogram by finding the value of x.

Step-by-step explanation:

The complete question is

m ∠ A = 100 - x

m ∠ B = 80 + x

m ∠ C = 110 - 3x

m ∠ D = 75 + 2x

Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are equal. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.

Options

A) x = 5

B) x = 7

C) x = 10

D) x = 15/2

we know that

In a parallelogram, opposite angles are parallel and consecutive angles are supplementary

so

m ∠ A=m ∠ C

m ∠ B=m ∠ D

m ∠ A+m ∠ B=180°

m ∠ B+m ∠ C=180°

step 1

Find the value of x

we know that

m ∠ A=m ∠ C

substitute the given values

solve for x

Group terms

Combine like terms

step 2

Verify the measure of the angles

therefore

---> is ok

---> is ok

---> is ok

---> is ok

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

answer: 12

step-by-step explanation: