Question

M/HCB = 60°, m/DCB = 9x-1, and m/DCH = 2x+ 16. Find x​

Answer 1

x=11

Explanation:

<DCB = <DCH + < HCB

9x-1 = 2x+16 + 60

Combine like terms

9x-1 = 2x+76

Subtract 2x from each side

9x-1-2x= 2x+76-2x

7x-1 = 76

Add 1 to each side

7x-1 +1 = 76+1

7x = 77

Divide by 7

7x/7 = 77/7

x=11

Answer 2

`x=11`

Explanation:

Note that ∠DCB is the sum of ∠HCB and ∠DCH. Hence:

`m\angle DCB = m\angle HCB + m\angle DCH`

Substitute in the appropriate values/expressions:

`(9x-1) = (60) + (2x+16)`

Solve for x. Combine like terms:

`9x - 1 = 2x + 76`

Subtract 2x from both sides:

`7x - 1 = 76`

Add one to both sides:

`7x = 77`

And divide. Hence:

`x=11`