Question

in the parallelogram below find the value of each variable. hint: find the value of t first.
$t =$ type your answer...
$r =$ type your answer...
$s =$ type your answer...

Explanation:

Step1: Set equal consecutive angles

In a parallelogram, consecutive angles are supplementary, so:
$$(3t - 15) + (2t + 10) = 180$$

Step2: Simplify and solve for t

Combine like terms and isolate t:
$$5t - 5 = 180$$
$$5t = 185$$
$$t = \frac{185}{5} = 37$$

Step3: Solve for r using opposite angles

Opposite angles in a parallelogram are equal:
$$4r = 2t + 10$$
Substitute $t=37$:
$$4r = 2(37) + 10 = 74 + 10 = 84$$
$$r = \frac{84}{4} = 21$$

Step4: Solve for s using opposite angles

Opposite angles in a parallelogram are equal:
$$3s = 3t - 15$$
Substitute $t=37$:
$$3s = 3(37) - 15 = 111 - 15 = 96$$
$$s = \frac{96}{3} = 32$$

Answer:

$t = 37$
$r = 21$
$s = 32$