CPhill

Very nice, RP !!!!

9 is correct

Let's look at the second one

(7x + 9) * 2 =  46      divide both sides by 2

7x + 9 =  23           subtract 9 from both sides

7x = 14

x = 2

In general

"Surface" area usuall refers to total surface area of an object

"Lateral" surface area is the total area less the areas of the "top" and "bottom" of an object

For example....the lateral surface area of a soup can is just the area of the label

The total surface area also includes the area of the top and bottom

Correct !!!

Agreed....all those lines make me crazy, too!!!

x+ 20+10x = 20 + 9x      simplify each side

11x + 20  = 20 + 9x       subtract  9x, 20 from both sides

2x = 0      divide  both sides by 2

x = 0

We are only really using two theorems here

1)   Opposite angles in a cyclic quadrilateral  sum to 180°

2)  The measure of an inscribed angle =  (1/2) the measure of the arc it intercepts

Second one

Notice that angle Q intercepts  arc PSR

And the measure of this arc= 137 + 41  =  178°

And because angle Q is an inscribed angle intercepting this arc...it measures (1/2)(arc PSR) = (1/2)(178) = 89°

We have a cyclic quadrilateral....R is supplemental to 57°  =  180 - 57  =  123°

And S is supplemental to Q =   180 - 89  =  91°

Hey, RP....good to see you !!!

First one

We have a quadrilateral inscribed in a circle  (a cyclic quadrilateral).....whenever this is so....the opposite angles in the quadrilateral are supplementary (the sum to 180°)

So 

 A + C = 180

A  + 101 = 180    subtract  101 from both sides

A = 79°

Smillarly

B + D = 180

B + 68 = 180

B = 180 - 68

B = 112°

LOL!!!!

EP  only paid a SMALL amount for this endorsement!!!

{ Seriously....he's one of our best "Answerers"  }