Answer:
see explanation
Step-by-step explanation:
Since lines a and b are parallel, then
∠NMP and ∠MPQ are same side interior angles and are supplementary, thus
a + a - 20 = 180
2a - 20 = 180 ( add 20 to both sides )
2a = 200 ( divide both sides by 2 )
a = 100, hence
∠NMP = a = 100° and
∠MPQ = a - 20 = 100 - 20 = 80°
Answer:
13. A tenth of a pound per bag. 14. Each friend will receive 1/6 of the total cake.
Answer:
Step-by-step explanation:
If the second angle's measure is based on the first angle's measure, and the third angle's measure is also based on the first angle's measure, then the first angle is the main angle. We will call that x.
1st angle: x
2nd angle: x + 20%
3rd angle: x - 20%
By the Triangle Angle-Sum Theorem, all those angles will add up to 180, so:
x + (x + 20%) + (x - 20%) = 180 and
3x = 180 so
x = 60. That means that
2nd angle: 60 + (.2*60) which is
60 + 12 = 72 and
3rd angle: 60 - (.2*60) which is
60 - 12 = 48. Let's check those angles. If
∠1 = 60
∠2 = 72
∠3 = 48,
then ∠1 + ∠2 + ∠3 = 180 and
60 + 72 + 48 does in fact equal 180, so you're done!
