In triangle QRS, measure of angle R is 20 degrees more than measure of angle Q and measure of angle S is 115 degrees more than measure of angle Q. Find measure of angle R.
the angles add to 180, so since
R=Q+20, Q=R-20
S=Q+115 = (R-20)+115 = R+95
Q+R+S=180
R-20 + R + R+95 = 180
...
Let's assume the measure of angle Q in triangle QRS is x degrees.
According to the given information, measure of angle R is 20 degrees more than measure of angle Q. So, angle R = x + 20 degrees.
Also, measure of angle S is 115 degrees more than measure of angle Q. So, angle S = x + 115 degrees.
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
angle Q + angle R + angle S = 180
Substituting the values we found earlier, we get:
x + (x + 20) + (x + 115) = 180
Simplifying the equation:
3x + 135 = 180
Subtracting 135 from both sides:
3x = 45
Dividing both sides by 3:
x = 15
Therefore, the measure of angle R is:
angle R = x + 20 = 15 + 20 = 35 degrees.
So, the measure of angle R in triangle QRS is 35 degrees.
To find the measure of angle R in triangle QRS, we need to first determine the measure of angle Q.
Let's assume that the measure of angle Q is x degrees.
From the given information, we know that the measure of angle R is 20 degrees more than the measure of angle Q. So, angle R = x + 20 degrees.
We also know that the measure of angle S is 115 degrees more than the measure of angle Q. Therefore, angle S = x + 115 degrees.
Now, we can use the fact that the sum of all angles in a triangle is 180 degrees.
In triangle QRS, we have:
angle Q + angle R + angle S = 180 degrees
Substituting the values we found earlier, we get:
x + (x + 20) + (x + 115) = 180
Simplifying the equation:
3x + 135 = 180
Subtracting 135 from both sides:
3x = 45
Dividing both sides by 3:
x = 15
Therefore, the measure of angle Q is 15 degrees.
To find the measure of angle R, we substitute the value of x in the equation we found earlier for angle R:
angle R = x + 20 = 15 + 20 = 35 degrees
Thus, the measure of angle R in triangle QRS is 35 degrees.