Question

For a craft project, Jackie cuts the two triangles described below out of fabric. Find the length of CE¯¯¯¯¯¯¯¯.

Answer 1

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,

$m\angle C=m\angle U$       (Given)

$m\angle E=m\angle V$       (Given)

$CD=UT$       (Given)

Two angles and a non -included side are equal in both triangle. So, both triangles are congruent by AAS postulate.

$\Delta CDE\cong \Delta UTV$

$CE=UV$                 (CPCTC)

$4z+7=13z-20$

$4z-13z=-7-20$

$-9z=-27$

Divide both sides by -9.

$z=3$

Now,

$CE=4(3)+7$

$CE=12+7$

$CE=19$

Therefore, the length of CE is 19 cm.

Answer 2

Answer:

19

Step-by-step explanation:

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