Question

The sum of the measures of anple X and anple Y is 90. If the measure of angle X is 30 less than

twice the measure of anple Y, what is the measure of angle X?

a)20°
b)359
c)50°
d)65

Answer 1

The measure of angle X can be found by setting up a system of equations and solving for X. The measure of angle Y is y, and the sum of X and Y is 90. By substituting the value of Y into the equation for X, we find that X = 50°.

Step-by-step explanation:

To find the measure of angle X, we can set up an equation using the given information. Let's say the measure of angle Y is y. According to the problem, the measure of angle X is 30 less than twice the measure of angle Y. This can be written as X = 2Y - 30.

We also know that the sum of the measures of angle X and angle Y is 90. So, we can set up another equation: X + Y = 90.

Now we can solve this system of equations to find the measure of angle X. Substituting the value of X from the first equation into the second equation, we get (2Y - 30) + Y = 90. Combining like terms, we have 3Y - 30 = 90. Adding 30 to both sides, we get 3Y = 120. Finally, dividing both sides by 3, we find Y = 40. Plugging this value back into the first equation to find X, we have X = 2(40) - 30 = 50.

Therefore, the measure of angle X is 50° (Option c).