What is the measure of a base angle in this figure?

a.41
b.21
c.31
d51

Explanation:

The base angles are congruent in this isosceles trapezoid, so 7x and 4x+9 are equal to each other

Let's solve for x

7x = 4x+9

7x-4x = 4x+9-4x subtract 4x from both sides

3x = 9

3x/3 = 9/3 divide both sides by 3

x = 3

If x were equal to 3, then

base angle = 7*x = 7*3 = 21

or

base angle = 4*x+9 = 4*3+9 = 12+9 = 21

Both base angles are 21 degrees each

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)

the graph on the bottom right