Question

quadrilateral efgh is a rhombus and $m\angle deh = 14t - 79^\circ$. what is the value of t? $t = \square^\circ$

Explanation:

Step1: Use rhombus diagonal property

In a rhombus, diagonals bisect the angles. So $\angle DEH = \angle EHD = 57^\circ$.

Step2: Set up equation for $t$

Set $14t - 79 = 57$.

Step3: Solve for $t$

Add 79 to both sides: $14t = 57 + 79 = 136$.
Divide by 14: $t = \frac{136}{14} = \frac{68}{7} \approx 9.71$, or simplify to integer check: $14t=136 \to t=\frac{68}{7}$

Answer:

$t = \frac{68}{7}$ (or approximately $9.71$)