   Chapter 5.3, Problem 31E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Δ A B F ∼ Δ C B D with obtuse angles at vertices D and F as indicated. If m ∠ B = 45 ° , m ∠ C = x and m ∠ A F B = 4 x , find x. Exercises 31, 32

To determine

To find:

The value of x in degree by using the given information.

Explanation

Definition:

CASTC:

Corresponding angles of similar triangles are congruent.

Description:

Given that ΔABFΔCBD with obtuse angles at vertices D and F as indicated. If mB=45°, mC=x and mAFB=4x.

The given figure is shown below.

Figure 1

From the given figure, it is observed that there are two triangles ABF and CBD and which is given that two triangles are similar.

Now draw the two triangles separately as shown below.

Figure 2

Figure 3

Since ΔABFΔCBD and from the definition of CASTC, corresponding angles of similar triangles are congruent

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