Question

1. which of the following statements is incorrect?

a fe = 58
b fe = 40
c x = 8
d df = 40

1. which of the following statements is incorrect?

a a triangle with three congruent sides is equiangular.
b the isosceles triangle theorem can be applied to equilateral triangles.
c the measure of each angle of an equilateral triangle is 120.
d a triangle with three congruent angles is equilateral.

1. in the figure shown, what is m∠a? explain.

a 57; △abc is an isosceles triangle with base angles a and c. m∠a = m∠c
b 66; △abc is an isosceles triangle with base angles b and c. m∠b = m∠c = 57, and m∠a + m∠b + m∠c = 180.
c 57; △abc is an equilateral triangle.
d there is not enough information to find m∠a.

1. an equiangular triangle has one side of length six inches. what is the perimeter of the triangle, in inches?

1. what are the measures of the angles in the triangle?

a 60; 60; 60
b 78; 51; 51
c 34; 112; 112
d 112; 34; 34

Explanation:

1.

Step1: Solve for \(x\)

Since the triangle is isosceles, \(8x - 34=40\).

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Or \(8x-34 = 6x + 10\)

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If \(8x-34 = 6x + 10\), then \(x = 22\). \(FE=6x+10=6\times22 + 10=142
eq58\)

2.

Step1: Recall properties of equilateral triangles

In an equilateral triangle, each angle is \(60^{\circ}\) (since the sum of angles in a triangle is \(180^{\circ}\) and all angles are equal). So the statement “The measure of each angle of an equilateral triangle is \(120\)” is incorrect.

3.

Step1: Use angle - sum property of a triangle

In an isosceles triangle \(\triangle ABC\) with \(AB = AC\), base angles \(B\) and \(C\) are equal. Given \(m\angle B=m\angle C = 57^{\circ}\).
By the angle - sum property of a triangle \(m\angle A+m\angle B+m\angle C=180^{\circ}\)

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4.

Step1: Recall properties of equiangular triangles

An equiangular triangle is also equilateral. If one side \(a = 6\) inches, then the perimeter \(P=3a\)

$$P = 3\times6=18$$

inches

5.

Step1: Use angle - sum property of a triangle

Since the triangle is isosceles (two sides are equal), let \((x + 17)=(4x-34)\)

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The angles are: \(x + 17=17+17 = 34^{\circ}\), \(4x-34=4\times17-34=34^{\circ}\), \(6x + 10=6\times17+10=112^{\circ}\)

Answer:

1. A. \(FE = 58\)
2. C. The measure of each angle of an equilateral triangle is \(120\).
3. B. \(66\); \(\triangle ABC\) is an isosceles triangle with base angles \(B\) and \(C\). \(m\angle B=m\angle C = 57\), and \(m\angle A+m\angle B+m\angle C=180\).
4. \(18\)
5. D. \(112\); \(34\); \(34\)