Chapter 4.2, Problem 40E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

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

# R S T V is a kite, with R S ¯ ⊥ S T ¯ and R V ¯ ⊥ V T ¯ . If m ∠ S T V = 40 ° , how large is the angle formeda) by the bisectors of ∠ R S T and ∠ S T V ? b) by the bisectors of ∠ S R V and ∠ R S T ?

To determine

a)

The angle formed by the bisectors of RST and STV.

Explanation

Calculation:

Given,

RSTV is a kite

RSÂ¯âŠ¥STÂ¯

RVÂ¯âŠ¥VTÂ¯

mâˆ STV=40Â°

Let the bisectors of âˆ RST and âˆ STV intersect at â€˜Oâ€™.

Now, we need to find the angle formed by the bisectors OS and OT, which is âˆ TOS.

In the kite âˆ T and âˆ S are bisected, thus in âˆ†TOS,

âˆ OST=90Â°2=45Â°, and

âˆ STO=40Â°2=20Â°

To determine

b)

The angle formed by the bisectors of SRV and RST.

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