The values of all the required angles are; m∠5 = 42°; m∠8 = 138°; m∠10 = 138° and m∠11 = 42°
How to Identify corresponding angles?
Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines.
Now, we are given that; m∠1 = 42°
By corresponding angles, we can say that;
m∠1 = m∠5
Thus; m∠5 = 42°
Now, we know that sum of angles on a straight line is equal to 180° i.e. they are supplementary angles.
Now, from the diagram, we can see that m∠5 and m∠8 are supplementary angles and as such;
m∠5 + m∠8 = 180°
42 + m∠8 = 180
m∠8 = 180° - 42°
m∠8 = 138°
Now, m∠9 is a corresponding angle to both m∠1 and m∠5. Thus, we can say that; m∠9 = 42°. However, m∠9 is supplementary to m∠10. Thus;
m∠10 = 180 - 42
m∠10 = 138°
Lastly, m∠10 and m∠11 are supplementary angles and as such;
m∠10 + m∠11 = 180°
138 + m∠11 = 180
m∠11 = 180° - 38°
m∠11 = 42°
Read more about Corresponding Angles at; https://brainly.com/question/2009183
#SPJ1
