Question

if ( gi = 3a - 59 ) and ( gk = 2a - 31 ), find the value of ( a ) in parallelogram ( hijk ).

Explanation:

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $GI = GK$.

Step2: Set up equation

$3a - 59 = 2a - 31$

Step3: Solve for $a$

Subtract $2a$ from both sides: $3a - 2a - 59 = -31$
Simplify: $a - 59 = -31$
Add 59 to both sides: $a = -31 + 59$

Answer:

$28$