If QRST below is a rectangle, find x if angle S is equal to 7x + 55.
90=7x+55
x=5 degrees
To find the value of x, we need to use the fact that the sum of all angles in a rectangle is always 360 degrees.
In a rectangle, opposite angles are equal. Therefore, angle R is also equal to angle S.
We are given that angle S is equal to 7x + 55. Since angle R is equal to angle S, we can set up the following equation:
7x + 55 = angle R
Since opposite angles in a rectangle are equal, angle R is also equal to angle Q.
Now we have two angles, R and Q, that are both equal to 7x + 55. We can set up another equation:
7x + 55 = angle Q
Since the sum of all angles in a rectangle is 360 degrees, we can set up the following equation:
angle Q + angle R + angle S + angle T = 360
Substituting the values of angle Q and angle R, we have:
(7x + 55) + (7x + 55) + (7x + 55) + angle T = 360
Now we can solve for x.
Combine like terms:
21x + 165 + angle T = 360
Subtract 165 from both sides:
21x + angle T = 195
Subtract angle T from both sides:
21x = 195 - angle T
We don't have enough information to determine the value of angle T, so we cannot solve for x.