Question

The difference between a number and 12 is 20. Ten times the sum of half a number and 6 is 8. Two-thirds of a number plus 4 is 7. One angle is six degrees more than twice another angle. The two angles added together equal 180 degrees. Find the measure of each angle.

a. x=28,y=152
b. x=32,y=148
c. x=20,y=160
d. x=18,y=162

Answer 1

The measure of each angle is b. x=32,y=148 .

Step-by-step explanation:

Let's represent the unknown numbers by x and y , and set up equations for each statement.

1. "The difference between a number and 12 is 20":

`\[ x - 12 = 20 \]`

2. "Ten times the sum of half a number and 6 is 8":

`\[ 10 * \left((x)/(2) + 6\right) = 8 \]`

3. "Two-thirds of a number plus 4 is 7":

`\[ (2)/(3)x + 4 = 7 \]`

4. "One angle is six degrees more than twice another angle. The two angles added together equal 180 degrees":

y = 2x + 6

x + y = 180

Now, solve this system of equations. The correct answer should satisfy all of these equations.

By solving the system, you should find that x = 32 and y = 148.

So, the correct answer is: b. x=32, y=148