Question

Parallel line theorem. Find unknown angles indicated and show work.

Answer 1

step 1

Find out the value of a

we have that

a=81 degrees -----> by alternate interior angles

step 2

Find out the value of b

we have

b+68=180 degrees ----> by form a linear pair (supplementary angles)

b=180-68

b=112 degrees

step 3

Find out the value of c

we have that

c=b -----> by corresponding angles

so

c=112 degrees

step 4

Find out the value of d

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

d+68+81=180

d+149=180

d=180-149

d=31 degrees

step 5

Find out the value of e

we have that

e=68 degrees -----> by corresponding angles