Question

if cd = 3a - 77 and cf = 2a - 43, find the value of a in rhombus defg.

Explanation:

Step1: Use rhombus diagonal property

In a rhombus, the diagonals bisect each other, so $CD = CF$.

Step2: Set up equation

Substitute the given expressions:
$3a - 77 = 2a - 43$

Step3: Solve for $a$

Subtract $2a$ from both sides:
$3a - 2a - 77 = -43$
$a - 77 = -43$
Add 77 to both sides:
$a = -43 + 77$
$a = 34$

Answer:

$34$