Question

find ( mangle k ) in rhombus ( hijk ).
( mangle k = square^circ )

Explanation:

Step1: Use rhombus consecutive angles property

Consecutive angles in a rhombus are supplementary, so:
$$(2p+24^\circ)+(3p-84^\circ)=180^\circ$$

Step2: Simplify and solve for $p$

Combine like terms and isolate $p$:
$$5p - 60^\circ=180^\circ$$
$$5p=240^\circ$$
$$p=48^\circ$$

Step3: Substitute $p$ into $\angle K$ expression

Calculate $m\angle K$ using $p=48^\circ$:
$$m\angle K=2(48^\circ)+24^\circ$$

Answer:

$120^\circ$