Question

Given ABC , DEF find the values of X and Y

Answer 1

Here, at least ABC and DEF are similar

Then

D = A = 87

=> 5x+2 =87

=> 5x =85

=> x =17

C = F = 180-D-E = 180-42-87=51

=> 3y = 51

=> y = 17

Answer 2

`y = 17`

`x = 17`

Explanation:

triangle ABC and DEF are similar and will therefore have the same angles.

the sum of all the angles on ANY triangle will ALWAYS add up to 180°

To work out what y equals, we must first find out what ∠B equals.

∠B corresponds with ∠E therefore, we know that ∠B = 42°

As we already have ∠A, we can now calculate ∠C.

180 - 42 - 87 = 51

∴∠C = 51°

to calculate
`y`:

`3y = 51`

divide both sides by 3. the 3 on the left gets cancelled out and 51 becomes 17

`y = 17`

to work out what
`x` equals, we know that ∠E = 42° and that ∠F = 51°

180 - 42 - 51 = 87

∠D = 87°

to calculate
`x`:

`5x + 2 = 87`

subtract 2 from both sides

`5x = 85`

divide both sides by 5

`x = 17`

I hope this helps :-)