Answer:
see explanation
Explanation:
∠ 1 and ∠ 5 are same- side exterior angles and sum to 180° , that is
∠ 1 + ∠ 5 = 180° , so
114° + ∠ 5 = 180° ( subtract 114° from both sides )
∠ 5 = 66°
------------------------------------------
∠ 1 and ∠ 2 are vertically opposite angles and are congruent ( equal ) , so
∠ 2 = ∠ 1 = 114°
-------------------------------------------
∠ 1 and ∠ 3 are corresponding angles and are congruent , so
∠ 3 = ∠ 1 = 114°
---------------------------------------------
∠ 3 and ∠ 4 are vertically opposite angles and are congruent , so
∠ 4 = ∠ 3 = 114°
----------------------------------------------
∠ 4 and ∠ 6 are a linear pair and sum to 180° , so
∠ 4 + ∠ 6 = 180° , then
114° + ∠ 6 = 180° ( subtract 114° from both sides )
∠ 6 = 66°
-----------------------------------------------
∠ 6 and ∠ 7 are alternate angles and are congruent , so
∠ 7 = ∠ 6 = 66°
--------------------------------------------
∠ 5 = 66° , ∠ 2 = 114° , ∠ 3 = 114° , ∠ 4 = 114° , ∠ 6 = 66° , ∠ 7 = 66°