Mathematics: 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°. ???

B. Between 1990 and 2015 cut in half the number of people whose income is less than $1.25 a day.Explanation:...

For a craft project, Jackie cuts the two triangles

afosburgh20

11.02.2022

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.

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