Exercise 6 Page 378

Consider the given triangle and its measures.

In the given figure, we can see that WX is congruent to WY. Let's identify the type of the given triangle by recalling the classification of triangles.

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^(∘).

Since the given triangle has two congruent sides, we can say that triangle WXY is an isosceles triangle. Then, we can consider the Isosceles Triangle Theorem to find the value of the variable x. The theorem states the following.

Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Using the theorem, we can conclude that ∠ YXW ≅ ∠ WYX. This means that both angles have the same measure. Therefore, we can equate them and write an equation that helps us find x. m∠ YXW = m∠ WYX Let's substitute m∠ YXW = 62 and m∠ WYX= 4x-2 in the above equation and solve it for x.

m∠ YXW = m∠ WYX

SubstituteII

m∠ YXW= 62, m∠ WYX= 4x-2

62= 4x-2

AddEqn

LHS+2=RHS+2

64=4x

DivEqn

.LHS /4.=.RHS /4.

16=x

RearrangeEqn

Rearrange equation

x=16

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