Answer:
Part A: (x+33) + (2x) = 90
Part B: mAngle 1= 52, mAngle 2= 38
Step-by-step explanation:
Part A:
To write an equation, we first must understand what we are trying to describe/equal to. In the figure, we can see a box in the bottom left corner. This signifies that the angle is a right angle, which equals to 90 degrees.
In the directions, it gives us the measurement of the two angles that make up that 90 degree angle, which is angle 1 and angle 2.
Angle 1 equals to x+33 and angle 2 equals to 2x.
Thus, we can say (x+33) + (2x) equals to 90 degrees.
Part B:
Now, we must solve for the angles. Simply, we must find the value of "x."
To do that, we add like terms on both sides of the equation:
(x+33) + (2x) = 90 becomes 3x + 33 = 90
There are two ways you can proceed from here: factor and solve, or simply the old fashioned way: elimination.
Factor and solve:
3x + 33 = 90 becomes 3(x+11)=3(30). I simply factored the LCD (largest common denominator) from both sides. If we multiply it out, we'll return to 3x + 33 = 90 We then proceed to divide both sides by three, giving us x+11=30. x equals 19.
Elimination:
3x + 33 = 90 becomes 3x=57. I simply subtracted 33 from both sides. Then, isolate x by dividing by three, and x equals 19.
We aren't done just yet. Now, since we know what x equals, we must substitute 19 for x in angle 1 and angle 2.
(x+33) + (2x) = 90
(19+33) + [2(19)] = 90
52 + 38 = 90
So, measure of angle 1 is 52, and measure of angle 2 is 38.
Let me know if you have any questions.
