figure RSTU is a rectangle. if m of angle SUT = 3x + 6 and m of angle RUS = 5x - 4, find m of angle SUT
M of angle SUT= 39°
To find the measure of angle SUT, we need to set up an equation and solve for x.
Since RSTU is a rectangle, opposite angles are congruent. Therefore, angle SUT and angle RUS have the same measure.
Given:
m(angle SUT) = 3x + 6
m(angle RUS) = 5x - 4
Since both angles have the same measure, we can set up the equation:
3x + 6 = 5x - 4
To solve this equation, let's simplify and isolate the x term:
3x - 5x = -4 - 6
-2x = -10
Now, let's solve for x by dividing both sides of the equation by -2:
x = (-10)/(-2)
x = 5
Now that we have found the value of x, we can substitute it back into the equation for angle SUT:
m(angle SUT) = 3x + 6
m(angle SUT) = 3(5) + 6
m(angle SUT) = 15 + 6
m(angle SUT) = 21
Therefore, the measure of angle SUT is 21 degrees.
To find the measure of angle SUT in rectangle RSTU, we need to use the fact that the sum of angles in a rectangle is 360 degrees.
In this case, we are given that angle RUS and angle SUT are adjacent angles in the rectangle. Therefore, their sum must be equal to 180 degrees (since a rectangle has four right angles, and the sum of the angles adjacent to a right angle is 180 degrees).
So, we can set up an equation:
m(angle RUS) + m(angle SUT) = 180 degrees
Given that m(angle RUS) = 5x - 4, we can substitute it into the equation:
(5x - 4) + m(angle SUT) = 180 degrees
Now, we can solve for the measure of angle SUT:
m(angle SUT) = 180 degrees - (5x - 4)
= 180 degrees - 5x + 4
= -5x + 184
Hence, the measure of angle SUT is -5x + 184.