Question

Which values of x and y make triangle CDE = triangle HFG?

Answer 1

Answer:

Option (4)

Step-by-step explanation:

By the property of congruence of the triangles given in the figure,

ΔCDE ≅ ΔHFG

By applying triangle sum theorem in ΔCDE,

m∠C + m∠D + m∠E = 180°

32° + 112° + m∠E = 180°

m∠E = 180° - 144°

m∠E = 36°

Corresponding side and angles of two congruent triangles are equal in measure.

Therefore, m∠E = m∠G

36° = (4y + 8)°

4y = 36 - 8

4y = 28

y = 7

Similarly, FG = DE

41 = 3x + 2

3x = 41 - 2

3x = 39

x = 13

Therefore, Option (4) will be the correct option.