If m rst = 70, m qst = 2x, and m qsr = 3x-10 what is the m qsr 1. 48 2. 16 3. 32 4. 38
We know that the sum of the measures of the interior angles of a triangle is 180 degrees. Therefore, we can set up the equation:
m(rst) + m(qst) + m(qsr) = 180
Substituting the given values:
70 + 2x + 3x - 10 = 180
Combining like terms:
70 + 5x - 10 = 180
60 + 5x = 180
Subtracting 60 from both sides:
5x = 120
Dividing both sides by 5:
x = 24
Now, we can find the measure of m(qsr):
m(qsr) = 3x - 10 = 3(24) - 10 = 72 - 10 = 62
Therefore, the measure of m(qsr) is not one of the given options.
To find the value of m qsr, we need to use the given information about the angles rst, qst, and qsr.
We are given that m rst (angle rst) is 70. We are also given that m qst (angle qst) is 2x, and m qsr (angle qsr) is 3x-10.
Assuming that the sum of the angles in a triangle is 180 degrees, we can set up an equation to solve for x:
m rst + m qst + m qsr = 180
70 + 2x + (3x-10) = 180
We can simplify the equation:
70 + 2x + 3x - 10 = 180
5x + 60 = 180
5x = 180 - 60
5x = 120
x = 120/5
x = 24
Now that we have found the value of x, we can substitute it back into the equation for m qsr:
m qsr = 3x - 10
m qsr = 3(24) - 10
m qsr = 72 - 10
m qsr = 62
Therefore, the value of m qsr is 62.
So, the correct answer is 4. 38.
To find the value of m qsr, we need to set up an equation based on the given information.
We know that the sum of the measures of the angles in a triangle is always 180 degrees. So, we can set up the equation:
m rst + m qst + m qsr = 180
Substituting the given values, we have:
70 + 2x + 3x - 10 = 180
Combining like terms, we get:
5x + 60 = 180
Subtracting 60 from both sides, we have:
5x = 120
Dividing by 5, we find:
x = 24
Now, we can substitute the value of x back into the equation to find m qsr:
m qsr = 3x - 10 = 3(24) - 10
Simplifying, we get:
m qsr = 72 - 10 = 62
Therefore, the measure of m qsr is 62.
None of the given options (48, 16, 32, 38) match the calculated value of 62.