find the measure of angel R in quadrilateral RSTW if the measure of angle R= 2x, the measure of angle S= x-7, the measure of angle T= x+5, and the measure of angle W= 30.
The angles of a quad add up to 360º
so
2x + x-7 + x+5 + 3- = 360
solve for x
Cyclic quads
To find the measure of angle R in quadrilateral RSTW, we need to add up the measures of all the angles in the quadrilateral and equate it to 360 degrees (since the sum of angles in a quadrilateral is always 360 degrees).
Let's use the given information to set up an equation:
Angle R = 2x
Angle S = x - 7
Angle T = x + 5
Angle W = 30
The sum of all the angles in the quadrilateral is given as:
Angle R + Angle S + Angle T + Angle W = 360
Substituting the given values, we have:
2x + (x - 7) + (x + 5) + 30 = 360
Now, let's simplify the equation:
2x + x - 7 + x + 5 + 30 = 360
Combining like terms:
4x + 28 = 360
To solve for x, we subtract 28 from both sides of the equation:
4x = 360 - 28
4x = 332
Dividing both sides of the equation by 4:
x = 332/4
x = 83
Now that we have found the value of x, we can substitute it back into the expression for angle R:
Angle R = 2x
Angle R = 2 * 83
Angle R = 166
Therefore, the measure of angle R in quadrilateral RSTW is 166 degrees.