In triangle RST, m<R = 5x -3, m<S = 3x + 2 and m<T = x+10. Find m<R
since R+S+T=180°
5x-3 + 3x+2 + x+10 = 180
9x +9 = 180
9x = 171
x = 19
m<R = 5x-3 = 92°
To find the measure of angle R (m<R), we can use the information given about the measures of angles S and T in triangle RST.
Angle R is opposite to side ST, angle S is opposite to side RT, and angle T is opposite to side RS.
In a triangle, the sum of the measures of the interior angles is always 180 degrees. We can use this information to set up an equation and solve for x.
m<R + m<S + m<T = 180
Substituting the given expressions for the measures of angles S and T:
(5x - 3) + (3x + 2) + (x + 10) = 180
Now, we can solve for x:
Combine like terms:
9x + 9 = 180
Subtract 9 from both sides:
9x = 171
Divide both sides by 9:
x = 19
Now that we have found the value of x, we can substitute it back into the expression for m<R to find its measure:
m<R = 5x - 3
m<R = 5(19) - 3
m<R = 95 - 3
m<R = 92
Therefore, the measure of angle R (m<R) is 92 degrees.