In parallelogram PQRS, angle P=(119-y)° and angle Q=(3y-15)°. Find the measure of angle S.
To find the measure of angle S in parallelogram PQRS, we need to remember that opposite angles in a parallelogram are congruent. This means that angle P and angle S are equal, as well as angle Q and angle R.
Given that angle P = (119 - y)° and angle Q = (3y - 15)°, we can set up an equation:
(119 - y)° = (3y - 15)°
Now, let's solve the equation for y:
119 - y = 3y - 15
First, let's simplify by combining like terms:
4y - y = 119 + 15
3y = 134
To isolate y, we divide both sides of the equation by 3:
y = 134/3
y ≈ 44.67
Now that we have found the value of y, we can substitute it back into the expression for angle P to find its measure:
angle P = 119 - y
= 119 - 44.67
≈ 74.33°
Since angle P and angle S are congruent, the measure of angle S is also approximately 74.33°.