The measure of an angle SUT is twice m<RUS. if m<RUS=(18x-8)degrees and m<TUS=(4x + 16) degrees. Find m<RUT. This is an acute angle. Please help. I have tried figuring this problem out a million and one ways. Thanks
The measure of an angle SUT is twice m∠RUS. if m∠RUS=(18x-8)degrees and m∠TUS=(4x + 16) degrees. Find m∠RUT. This is an acute angle. Please help. I have tried figuring this problem out a million and one ways. Thanks
its 30 degrees ya dink
well, surely you must recognize that ∠TUS ≅ ∠SUT, so that means that
4x+16 = 2(18x-8)
4x+16 = 36x-16
x = 1
So,
∠SUT = 20°
∠RUS = 10°
No idea what ∠RUT is, since you haven't said anything about the relative locations of the points or the angles.
m<SUT فأوجد، m<SUT=(3x+6),m<RUS=(5x-4) اذا كان
To find the measure of angle RUT, we first need to determine the values of m<RUS and m<TUS by substituting their expressions into the given equations.
Given:
m<RUS = 18x - 8 degrees
m<TUS = 4x + 16 degrees
Since the measure of an angle SUT is twice m<RUS, we have:
m<SUT = 2 * m<RUS
Substituting the expression for m<RUS, we can rewrite this as:
m<SUT = 2 * (18x - 8)
Now, we need to use the fact that the sum of the angles in a triangle adds up to 180 degrees:
m<RUS + m<TUS + m<RUT = 180
Substituting the given expressions, we have:
(18x - 8) + (4x + 16) + m<RUT = 180
Simplifying the equation, we get:
22x + 8 + m<RUT = 180
Now, isolate m<RUT by subtracting 22x and 8 from both sides of the equation:
m<RUT = 180 - 22x - 8
m<RUT = 172 - 22x
Since we know that angle RUT is an acute angle (meaning it is less than 90 degrees), we need to determine the range of values for x that make m<RUT less than 90 degrees.
Setting m<RUT < 90, we can solve the inequality:
172 - 22x < 90
First, subtract 172 from both sides:
-22x < 90 - 172
-22x < -82
Then, divide both sides by -22, remembering to reverse the inequality since we are dividing by a negative number:
x > (-82)/(-22)
x > 82/22
x > 41/11
Therefore, for angle RUT to be an acute angle, x must be greater than 41/11.
Finally, to find the specific measure of angle RUT, substitute the value of x in m<RUT = 172 - 22x:
m<RUT = 172 - 22 * (41/11)
m<RUT = 172 - 82
m<RUT = 90 degrees
Hence, the measure of angle RUT is 90 degrees.