Question

Find x and y. ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

Answer 1

• x = 36°

• y = 48°

Explanation:

Given:

• ΔABC ≅ ΔFDE

• We can tell that y = 48° because ΔABC ≅ ΔFDE.

• We can also tell that ∠DEF = 108 because ΔABC ≅ ΔFDE.

Let's first try to simplify ∠CAB in ΔABC. Then we can find the 'x' in ΔFDE with the help of ΔABC.

ΔABC = 108 + 48 + ∠CAB = 180°

=> 156 + ∠CAB = 180°

=> ∠CAB = 24°

=> 48 + 108 + 2x - 48 = 180°

=> 108 + 2x = 180°

=> 2x = 72°

=> x = 36°

So, after working on this problem, we can conclude that 'x = 36°' and 'y = 48°'. Hoped this helped.

Answer 2

Answer: x=36, y=48

Explanation:

The sum of the angles in a triangle is 180. From triangle ABC we see that:

108 + 48 + Z = 180, where Z is the unknown third angle.

156 + Z = 180

Z= 24 (angle CAB).

Since the triangles are similar, we can say angle EDF(y) is equal to angle CAB (48). Thus,

y = 48

we can also say that angle CAB is the same as angle DFE:

24 = (2x-y)

24=2x-48

72=2x

x=36