we have that
1) What is the measure in degrees of ∠ 1?
∠ 1+110=180----> ∠ 1=180-110---> ∠ 1=70°---> angles 1 and 110 are supplementary angles
2) What is the measure in degrees of ∠ 2?
∠ 2+115=180----> ∠ 2=180-115----> ∠ 2=65°---> angles 2 and 115 are supplementary angles
3) What is the measure in degrees of ∠ 3?
∠ 3=∠ 2----> ∠ 3=65°------> angles 3 and 2 are congruent by corresponding angles
4) What is the measure in degrees of ∠ 4?
∠ 4=115---> ∠ 4=115°----> angles 4 and 115 are congruent by corresponding angles
5) What is the measure in degrees of ∠ 6?
step 1
find the value of angle ∠7
we know that
∠1 +∠2 +∠7=180---------> (sum of the internal angles of a triangle
∠7=180-(∠1 +∠2)------> ∠7=180-(70+65)----------> ∠7=45°
∠6=∠7----------> ∠6=45°--------------> angles 6 and 7 are opposed by the vertex, so they are congruent.