Answer:
118°
Step-by-step explanation:
When two parallel lines are cut by a tranversal, then the exterior angles are supplimentary and the corresponding angles are congruent.
Therefore the angle above (15x - 17)° is also (5x + 17)° and the angle below (5x + 17)° is also (15x - 17)°.
Angles on a straight line adds up to 180°. So to know the measure of the larger angle we must both equations and equal it to 180° to find x in order to know the larger angle.
(5x + 17) + (15x - 17) = 180
5x + 15x + 17 - 17 = 180
20x = 180
20x/20 = 180/20
x = 9°
Nkw let's substitute x = 9 into the equations
5x + 17 =
5(9) + 17 =
= 62°
15x - 17 =
15(9) - 17 =
= 118°
Both equations should add up to be 180°.
Therefore the measure of the largest angle is 118°.
Answer: 11
Step-by-step explanation:
1/2.
divide everything by 9.
same as before, is the proportion of one, the same as the other? let's do the same here without much fuss.
![\bf \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{~~2\frac{1}{3}~~}{\frac{3}{4}}=\cfrac{~~4\frac{2}{3}~~}{1\frac{1}{2}}\implies \cfrac{~~\frac{7}{3}~~}{\frac{3}{4}}=\cfrac{~~\frac{14}{3}~~}{\frac{3}{2}}\implies \cfrac{7}{3}\cdot \cfrac{4}{3}=\cfrac{14}{3}\cdot \cfrac{2}{3}\implies \cfrac{28}{9}=\cfrac{28}{9}~~\textit{\Large \checkmark}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B3%7D%7B2%7D%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Ccfrac%7B~~2%5Cfrac%7B1%7D%7B3%7D~~%7D%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5Ccfrac%7B~~4%5Cfrac%7B2%7D%7B3%7D~~%7D%7B1%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B~~%5Cfrac%7B7%7D%7B3%7D~~%7D%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5Ccfrac%7B~~%5Cfrac%7B14%7D%7B3%7D~~%7D%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B7%7D%7B3%7D%5Ccdot%20%5Ccfrac%7B4%7D%7B3%7D%3D%5Ccfrac%7B14%7D%7B3%7D%5Ccdot%20%5Ccfrac%7B2%7D%7B3%7D%5Cimplies%20%5Ccfrac%7B28%7D%7B9%7D%3D%5Ccfrac%7B28%7D%7B9%7D~~%5Ctextit%7B%5CLarge%20%5Ccheckmark%7D)
ΔBED and Δ DEC are similar (AAA). Therefore we have the proportion:
<em>cross multiply</em>
