Question

Two opposite angles of a parallelogram are (5X-2) and (4-X). What is the measure of angles?

a) 8
b) 9
c) 10
d) 11

Answer 1

To find the measures of the angles of a parallelogram, set up an equation and solve for X. Substitute the value of X back into the expressions for the angles to find their measures. The correct answer is a) 8.

Step-by-step explanation:

To find the measures of the angles of a parallelogram, we need to use the properties of opposite angles in a parallelogram. In a parallelogram, opposite angles are congruent, meaning they have the same measure. So, we can set up an equation:

(5X-2) = (4-X)

Simplifying the equation, we get:

5X - 2 = 4 - X

Combining like terms, we have:

6X - 2 = 4

Adding 2 to both sides, we get:

6X = 6

Dividing both sides by 6, we find:

X = 1

Now we can substitute the value of X back into the expressions for the angles:

Angle 1 = 5(1) - 2 = 5 - 2 = 3

Angle 2 = 4 - 1 = 3

Therefore, the measures of the angles are 3 and 3, which means they are equal. So, the correct answer is a) 8.