Question

Please solve q 73 ?

Answer 1

`x=15^@`, therefore (1) is the right choice in q73.

Explanation:

The picture is a little hard to read, so I've created a diagram of the situation:

The question gives us the following information:
`AB=AC`, so `/_B=/_C`
`/_BAD=30^@`
`AD=AE` (`=>/_ADE=/_AED`)
We want to find `/_CDE=x`

To make it easier, let `/_B=b`, `/_DAE=a`, `/_DEA=e`
We have
`AB=AC => /_B=/_C=b`
`AD=AE => /_ADE=/_AED=e`

As the sum of the angles in a triangle = `180^@`, it follows that:
`/_A=a+30^@=180^@-2b`.
`=>a=150^@-2b` (1)

In `Delta ADE`: `/_EAD=180^@-(/_DEA+/_EDA)`
i.e. `a=180^@-2e` (2)

As (1) and (2) are two expressions for the same angle, it follows that
`180^@-2e=150^@ -2b`
`=>2e=2b+30^@ => e=b+15^@`

As `/_CED=180^@-e=180^@ - (b+15^@)=165^@-b`

Therefore
`x=180^@-(/_C+/_CED)=180^@-(b+165^@-b)=15^@`

The conclusion is therefore that
`x=15^@` and (1) is the right choice in q73.