We are given:
AB = 7x + 10
BD = 9x - 2
∠DBC = 9y - 9
∠ABC = 90°
AB = BD
Solving for x:
We are given that AB = BD
7x + 10 = 9x - 2 [since AB = 7x+10 and BD = 9x-2]
10 = 2x - 2 [subtracting 7x from both sides]
2x = 12 [adding 2 on both sides]
x = 6 [dividing both sides by 2]
Hence, x = 6
Solving for y:_______________________________________________
We know that AD is a straight line,
So, ∠ABC and ∠DBC must form a linear pair
∠ABC + ∠DBC = 180°
90 + 9y-9 = 180
9y - 9 = 90 [subtracting 90 from both sides]
9y = 99 [adding 9 on both sides]
y = 11 [dividing both sides by 9]
Hence, y = 11
