If m∠W = 105° and m∠Y = 75°, then m∠X =
Responses
A 10°.10°.
B 20°.20°.
C 30°.30°.
D 75°.75°.
E 120°.
Joseph completely covered the floor of his square office with carpet. He used 148 ft2 of carpet. Which measurement is closest to the length of one side of Joseph’s office in feet?
Responses
A 11 ft
B 27 ft
C 12 ft
D 74 ft
Since the office is square, all sides would have the same length.
Let's call the length of one side x.
The area of a square can be found by squaring the length of one side.
So, x^2 = 148
Taking the square root of both sides, we get x = √148 ≈ 12.16552506
Since we need to find the measurement closest to the length of one side, the closest measurement is 12 ft.
The correct answer is C. 12 ft.
To find the measure of angle X, we can use the fact that the sum of angles in a triangle is always 180°.
In this case, we have two angles given: m∠W = 105° and m∠Y = 75°. To find angle X, we need to subtract the sum of these two angles from 180°.
m∠X = 180° - (m∠W + m∠Y)
m∠X = 180° - (105° + 75°)
m∠X = 180° - 180°
m∠X = 0°
So, the measure of angle X is 0°.
None of the given options (A, B, C, D, E) is correct.
Since ∠W and ∠Y are supplementary angles, we know that their measures add up to 180°. ∠W + ∠Y = 180°.
Substituting the given angle measures, we have 105° + 75° = 180°.
This simplifies to 180° = 180°, which is true.
Therefore, we can conclude that the measure of ∠X is 180° - 105° = 75°.
The correct answer is D. 75°.