Question

If AB∥DC, then find the value of c if

m∠B=(4c+20) and
m∠C=(3c−15).
a.c=5
b.c=10
c.c=15
d.c=20

Answer 1

To find the value of ‘c’ when AB is parallel to DC and given the measures of angles B and C, we equate the expressions for the alternate interior angles and solve for ‘c’, finding that ‘c’ is 35.

Step-by-step explanation:

The question deals with finding the value of the variable c in the context of parallel lines and angle relationships. Given that line AB is parallel to line DC, and you have the measures of the angles at B and C expressed in terms of c (i.e., m∠B=(4c+20) and m∠C=(3c−15)), we can use the fact that alternate interior angles are equal when two lines are parallel and cut by a transversal.

Set the two expressions equal to each other because they represent the measures of alternate interior angles:

4c + 20 = 3c − 15

Solve for c:

Thus, the value of c is 35.