Answer:
1) Find the measure of each angle.
The measure of each angle = 63° and 27°
2) Which equation below accurately translates the sentence and could be used to find the measure of each angle?
a) 2x + 9 = 90 - x
Step-by-step explanation:
1) Find the measure of each angle.
Two Angles are Complementary when they add up to 90 degrees (a Right Angle)
Mathematically this is represented as:
x° + y° = 90°
From the above question, we are told that:
The measure of an angle is 9 more than twice its complement.
Let the complement of an angle be represented by x
And its measure of an angle be represented by y
Hence,
y = 2× x+ 9
y =(2x + 9)°
x° + y° = 90°
Substitute 2y + 9 for x
x + 2x + 9 = 90
Collect like terms
x + 2x = 90 - 9
3x = 81
Divide both sides by 3
3x/3 = 81/3
x = 27°
We find y(measure of the angle)
x + y = 90
27 + y = 90
y = 90 - 27
y = 63°
Therefore, the measure of each angle is given as:
Measure of an angle = 63°
Complement of an angle = 27°
2) Which equation below accurately translates the sentence and could be used to find the measure of each angle?
a)2x + 9 = 90 - x
b) x + 9 = 2(x - 90)
c) x = 9 + 2(90 - x)
d) 2x = (x - 90) + 9
Option a) is the correct option
