Question

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

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°.

Answer: ???

Answer 1

19

Explanation:

took the test

Answer 2

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.