Answer:
[tex]y = 17[/tex]
[tex]x = 17[/tex]
Step-by-step 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 [tex]y[/tex]:
[tex]3y = 51[/tex]
divide both sides by 3. the 3 on the left gets cancelled out and 51 becomes 17
[tex]y = 17[/tex]
to work out what [tex]x[/tex] equals, we know that ∠E = 42° and that ∠F = 51°
180 - 42 - 51 = 87
∠D = 87°
to calculate [tex]x[/tex]:
[tex]5x + 2 = 87[/tex]
subtract 2 from both sides
[tex]5x = 85[/tex]
divide both sides by 5
[tex]x = 17[/tex]
I hope this helps :-)
