Question

13/14

16 15
10
12 11
The diagram shows parallel lines a and b cut by
transversals c and d.
If m/1 = 123° and m/8= 110°, what is the measure of each of the following angles?
m/4=
m/10=>
m/16=
m/5=>
m/11=

Answer 1

Using the properties of parallel lines and transversals, we can find the measures of the missing angles:

m/1 = m/2 (alternate interior angles)

m/1 = m/5 + m/4 (interior angles on the same side of transversal c)

m/8 = m/5 (corresponding angles)

m/8 = m/7 + m/6 (interior angles on the same side of transversal d)

We can use these equations to solve for the missing angles:

m/4 = m/1 - m/5 = 123° - 10° = 113°

m/10 = m/1 - m/8 = 123° - 110° = 13°

m/16 = m/8 + m/7 + m/6 = 110° + m/7 + m/6

m/5 = m/8 = 110°

m/11 = m/1 - m/10 - m/5 = 123° - 13° - 110° = 0°

Note that m/11 is 0°, which means that line b and transversal c are parallel, and there is no intersection between them.