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Chapter 2: Q53. (page 117)

GEOMETRY If 螖LMNis similar to 螖LPO, what is z?

F 240

G 140

H 120

J 70

Short Answer

Expert verified

The value of z is 140.

Step by step solution

01

Step 1. Use the definition of similar triangles.

Twotrianglesaresimilarif they have the same ratio of corresponding sides and equal pairs of corresponding angles.

Since If 螖LMNis similar to螖LPO

We have

LNLO=LMLP=MNOP

02

Step 2. Solve for the missing side.

As the triangles are similar to each other, and we have

LNLO=LMLP=MNOP

To find OP=z, we plug the values and simplify as shown

180360=70z[Cross-multiply]180z=70360180z=25200

We further simplify, by dividing 180 both sides as shown:

180z180=25200180z=140

03

Step 3. Interpret the result.

The missing side OP=z has a measure of 140.

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