Given:
In triangle CDE, CD=7 cm, CE=(4z+7) cm, ∡C=48°, and ∡E=82°.
In triangle TUV, UV=(13z−20) cm, UT=7 cm, ∡U=48°, and ∡V=82°.
To find:
The length of CE.
Solution:
In triangle CDE and triangle UTV,
[tex]m\angle C=m\angle U[/tex] (Given)
[tex]m\angle E=m\angle V[/tex] (Given)
[tex]CD=UT[/tex] (Given)
Two angles and a non -included side are equal in both triangle. So, both triangles are congruent by AAS postulate.
[tex]\Delta CDE\cong \Delta UTV[/tex]
[tex]CE=UV[/tex] (CPCTC)
[tex]4z+7=13z-20[/tex]
[tex]4z-13z=-7-20[/tex]
[tex]-9z=-27[/tex]
Divide both sides by -9.
[tex]z=3[/tex]
Now,
[tex]CE=4(3)+7[/tex]
[tex]CE=12+7[/tex]
[tex]CE=19[/tex]
Therefore, the length of CE is 19 cm.
