Question

Geometry parallel lines (please solve and explain)

Answer 1

see explanation

Explanation:

∠ 1 and ∠ 2 are corresponding angles and are congruent , then

7x - 27 = 4x + 18 ( subtract 4x from both sides )

3x - 27 = 18 ( add 27 to both sides )

3x = 45 ( divide both sides by 3 )

so

∠ 1 and ∠ 2 = 7x - 27 = 7(15) - 27 = 105 - 27 = 78°

∠ 2 and ∠ 3 are corresponding angles and are congruent , then

∠ 3 = 78°

∠ 3 and ∠ 4 are same- side interior angles and sum to 180° , that is

78 + 4y + 2 = 180

4y + 80 = 180 ( subtract 80 from both sides )

4y = 100 ( divide both sides by 4 )

y = 25

thus

∠ 4 = 4y + 2 = 4(25) + 2 = 100 + 2 = 102°

in conclusion

x = 15 , y = 25 , ∠ 1 = 78° , ∠ 4 = 102°