Question

I'm confused on how to do this section, can someone help me out? My geometry teacher isn't very good at explaining things

Answer 1

Answer:

hey mate!!

Dont worry. i am here to explain u.

*for figure see the attachment*

So,

a) Value of y

=> As you can see in the figure, 2 lines AB and CD are intersecting each other at F(look at the top).

Now,

=> angle AFD = angle CFB (they r vertically opposite angles and are always equal)

so,

=> 72° = 8y - 16

=> 8y = 88°

=> y = 11°

b) measure of angle 1

=> angle 1 = angle DFB (just named it)

=> we know that the line AB is straight , and hence total angles' sum is 180°

=> angle AFD + angle DFB = 180° (this is known as linear pair)

=> 72 + angle DFB = 180

=> angle DFB = 108°

=> measure of angle 1 = 108°

c) measure of angle 2

=> angle 2 = angle AFE

=> As CD is a straight line too,

=> angle DFA + angle AFE + angle EFC = 180 (linear pair)

=> 72 + angle AFE + 40 = 180

=> angle AFE = 180 - 112

=> angle AFE = 68°

=>measure of angle 2 = 68°

d) Value of x

=> As AC is a straight line too,

=> angle AEF + angle FEC = 180 (linear pair)

=> (10x - 24) + 90 = 180 ------(remember the angle marked like the one at angle FEC or the box type is always 90°)

=> 10x - 24 = 90

=> 10x = 114

=> x = 11.4°

HOPE U UNDERSTOOD IT!!!

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