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Geometric Angle and Average Arithmetic Mean w/variable probs

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by GMatt08 » Wed Mar 12, 2008 12:33 pm
Hey everyone,

Anyone care to explain these ones? Not finding much in the way of help through google searches!

Thanks,

-Matt

In triangle ABC, AB=BC and (C’s measure is 65°.) What is the measure of angle B?


A 40°
B 50°
C 60°
D 65°
E 75°

--------

If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x?


A 3
B 15
C 17
D 35
E 42
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by tmmyc » Wed Mar 12, 2008 12:47 pm
1.

The geometry concept being test here is:

"If a triangle has two sides that are equal, the two angles opposite those sides are also equal."

If AB = BC, then the angles opposite those two sides are equal, namely angle C and angle A.

Since angle C is 65 degrees, angle A is also 65 degrees.

Angle B is then 180 - 65 - 65 = 50.
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by tmmyc » Wed Mar 12, 2008 12:53 pm
2.

Convert the word problem into mathematical statements.

Average arithmetic mean of 8, 12, 15, 21, x and 11...

(8 + 12 + 15 + 21 + x + 11) / 6


...is 17

(8 + 12 + 15 + 21 + x + 11) / 6 = 17


What is x?

(8 + 12 + 15 + 21 + x + 11)/ 6 = 17
-> 8 + 12 + 15 + 21 + x + 11 = 102
--> x = 102 - (8 + 12 + 15 + 21 + 11)
---> x = 102 - 67
----> x = 35
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