Exercise 37 Page 547

An extended ratio compares three or more numbers. We want to find the measures of the angles of a quadrilateral that fit the given extended ratio. 2 : 4 : 6 : 3 This means that we can express the measures of the angles of the quadrilateral as 2x, 4x, 6x, and 3x.

By the Polygon Angle Sum Theorem, we know that the sum of the measures of the angles of a quadrilateral is 360^(∘). 2x + 4x + 6x + 3x=360 Let's solve this equation and find x.

2x+4x+6x+3x=360

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Solve for x

AddTerms

Add terms

15x=360

DivEqn

.LHS /15.=.RHS /15.

x=24

Now, to find the measure of each angle of the triangle, we will substitute x=24 into the expressions for each of the angle measures.

Expression	Substitute	Simplify
2x	2(24)	48
4x	4(24)	96
6x	6(24)	144
3x	3(24)	72

The measures of the angles are 48^(∘), 96^(∘), 144^(∘), and 72^(∘).