The angle measurements in the diagram are represented by the following expressions.
1 answer:
Given:
To find:
The value of x and measure of ∠A.
Solution:
Let C be angle the vertically opposite to ∠A.
The reference image for answer is attached below.
By vertical angle theorem:
m∠A = m∠C
m∠C = 10x + 24°
By the corresponding angle theorem:
m∠C = m∠B
Subtract 24° on both sides.
Subtract 6x from both sides.
Divide by 4 on both sides.
The value of x is 12°.
The measure of ∠A is 144°.
You might be interested in
First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27). But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing. The first derivative of the function is 
. Set the derivative equal to 0 and factor to find the critical numbers. 
, so x = -3 and x = 1/3. We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing. From there we will look at our points to determine which fall into the "decreasing" category. Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞. In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval. In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval. In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval. In order to determine where our points in question fall, look to the x value. The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12). The point (-3, -18) is already a min value.