Exercise 38 Page 341

The triangle appears to be obtuse, but since the diagram may not be to scale, we need to find the angle measures. To do so, we will start by finding the value of x.

Finding x

The Triangle Angle-Sum Theorem tells us that the measures of the interior angles of a triangle add up to 180^(∘). Let's set the sum of the given expressions equal to 180^(∘) and solve the resulting equation for x. For simplicity, we will ignore the degree symbol for this calculation.

(15x+1)+(6x+5)+(4x-1)=180

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Solve for x

RemovePar

Remove parentheses

15x+1+6x+5+4x-1=180

AddTerms

Add terms

25x+5=180

SubEqn

LHS-5=RHS-5

25x=175

DivEqn

.LHS /25.=.RHS /25.

x=7

Classifying the Triangle

To classify the triangle by its angles, we will substitute x=7 into the expressions to find the angle measures.

Expression	Angle Measure	Angle Type
15x+1	15(7)+1=106	obtuse
6x+5	6(7)+5=47	acute
4x-1	4(7)-1=27	acute

Since one of the angles is obtuse, this is an obtuse triangle.

Extra

Classification of Triangles

Triangles can be classified either according to their side lengths or to their internal angle measures.

The following table lists all the different types of triangles by their corresponding classification.

Classification of Triangles
Scalene Triangle	A scalene triangle is a triangle in which all three sides have different lengths.
Isosceles Triangle	An isosceles triangle is a triangle that has two congruent sides.
Equilateral Triangle	An equilateral triangle is a triangle in which all the sides are congruent.
Acute Triangle	An acute triangle is a triangle where all angles are less than 90^(∘) or π2.
Obtuse Triangle	An obtuse triangle is a triangle with exactly one an angle whose measure is greater than 90^(∘) or π2.
Right Triangle	A right triangle is a specific type of triangle that contains one angle of 90^(∘).

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Finding x

Classifying the Triangle

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