What are the values of m∠abc, m∠cbf, m∠abd and m∠dbe in the given figure? explain or show your work.

answer:

step-by-step explanation:

angle abc = 60 degrees

angle cbf = 120 degrees

angle abd = 90 degrees

angle dbe = 30 degrees

work shown:

angle abd = w = 90 degrees as shown by the square angle marker.

angles w, x and 60 form a straight angle, so they add to 180

w+x+60 = 180

90+x+60 = 180

x+150 = 180

x = 180-150

x = 30, which is angle dbe

an alternative is to note how x+60 = 90, so that leads to x = 30.

angles y, w and x form a straight angle as well

y+w+x = 180

y+90+30 = 180

y+120 = 180

y = 180-120

y = 60, which is angle abc

a shortcut is to note how angle abc and ebf are vertical angles, and that ebf is 60 degrees (recall that all vertical angles are congruent).

there are a few ways to find the value of z

first is to solve y+z = 180 for z

y+z = 180

60+z = 180

z = 180-60

z = 120, which is angle cbf

or,

note how angle (w+x) is vertical to angle z

w+x = 90+30 = 120

so this is another way to see how z = 120.

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