In the figure, x is an exterior angle to triangle abc. (a) explain why x is equal to the sum of the measures of the two nonadjacent interior angles. (b) what is m

Hello from MrBillDoesMath!

a) See Discussion below

b) Don't know what "m" refers to

Discussion:

Part a)

A triangle contains 180 degrees.

A + B + C = 180   (*)

where A is the angle inside the triangle.

From the diagram

B +C =   62 + 78 = 140

Substituting this in (*) gives

A + (140) = 180      => subtract 140 from both sides

A = 180 - 140 = 40

Now a line has 180 degrees so x + A = 180. But A = 40 (shown above) so x+ 40 = 180, or x = 140. That is, x  = 140 - the sum of the measures of the two nonadjacent interior angles

Part b)

I can't answer this part is it is unclear what "m" refers to. Sorry.

Thank you,

MrB

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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