Question

find ( mangle t ) in rhombus ( tuvw ).
( mangle t = square^circ )

Explanation:

Step1: Use rhombus consecutive angles property

Consecutive angles in a rhombus are supplementary, so:
$$(2y-24) + y = 180$$

Step2: Solve for y

Combine like terms and isolate y:
$$3y - 24 = 180$$
$$3y = 204$$
$$y = 68$$

Step3: Find $\angle V$ first

Substitute y into $\angle V$ expression:
$$m\angle V = 2(68) - 24 = 112^\circ$$

Step4: Use rhombus opposite angles property

Opposite angles in a rhombus are equal, so $\angle T = \angle V$.

Answer:

$112$