Question

find m∠j in rhombus hijk. m∠j = °

Explanation:

Step1: Recall property of rhombus

Adjacent angles of a rhombus are supplementary. So $\angle H+\angle K = 180^{\circ}$. Given $\angle H=a$ and $\angle K=a + 80^{\circ}$, we have $a+(a + 80^{\circ})=180^{\circ}$.

Step2: Solve for $a$

Combine like - terms: $2a+80^{\circ}=180^{\circ}$. Subtract $80^{\circ}$ from both sides: $2a=180^{\circ}-80^{\circ}=100^{\circ}$. Divide both sides by 2: $a = 50^{\circ}$.

Step3: Find $\angle J$

Opposite angles of a rhombus are equal. $\angle J=\angle H$. Since $a = 50^{\circ}$, $\angle H = 50^{\circ}$, so $\angle J=50^{\circ}$.

Answer:

$50$