Question

Unit 4 homework 3 Gina Wilson pls help w homework!

Answer 1

Answer/Step-by-step explanation:

1. An isosceles ∆ has two equal sides. The base angles of an isosceles ∆ are also equal.

Therefore:

m<U = 54° (base angle of isosceles ∆)

m<T = 180 - (54 + 54) (sum of ∆)

m<T = 72°

2. ∆LMN is an isosceles ∆, therefore:

m<M = ½*(180 - 28) = 76°

m<N = m<M (base angle of isosceles)

m<N = 76°

3. ∆FEG is an isosceles ∆, because it has two equal base angles.

Therefore:

EF = FG

EF = 18 in

m<F = 180 - (23 + 23) = 134°

4. ∆PQR is an equilateral ∆. All sides and angles of an equilateral ∆ are equal.

Therefore:

m<P = 60°

m<Q = 60°

m<R = 60°

5. 4x + 23 = 10x - 1 (2 asides of an isosceles ∆ are equal)

Collect like terms

4x - 10x = -23 - 1

-6x = -24

Divide both sides by -6

x = 4

6. 2*(9x - 25) = 180 - 104 (base angles of isosceles ∆)

18x - 50 = 76

Add 50 to both sides

18x = 76 + 50

18x = 126

Divide both sides by 18

x = 7

7. 5x - 7 = 8x - 55 (base angles of an isosceles)

Collect like terms

5x - 8x = 7 - 55

-3x = -48

Divide both sides by -3

x = 16

8. 4x + 8 = 60° (angle of an equilateral ∆)

Subtract 8 from each side

4x = 60 - 8

4x = 52

Divide both sides by 4

x = 13

Answer 2

Angles in a triangle may or may not be congruent.

1. Triangle STU

Triangle STU is an isosceles triangle.

So:

$\mathbf{\angle T = \angle U}$

This gives

$\mathbf{\angle T + \angle U + \angle S = 180}$ --- sum of angles in a triangle

Substitute $\mathbf{\angle T = \angle U}$

$\mathbf{\angle T + \angle T + \angle S = 180}$

$\mathbf{2\angle T + 54 = 180}$

Subtract 54 from both sides

$\mathbf{2\angle T= 126}$

$\mathbf{\angle T= 63}$

So:

$\mathbf{\angle T = 63}$ and $\mathbf{\angle U = 63}$

2. Triangle LMN

Triangle LMN is an isosceles triangle.

So:

$\mathbf{\angle M = \angle N}$

This gives

$\mathbf{\angle L+ \angle M + \angle N = 180}$ --- sum of angles in a triangle

Substitute $\mathbf{\angle M = \angle N}$

$\mathbf{\angle L + \angle M + \angle M = 180}$

$\mathbf{2\angle M + 28 = 180}$

Subtract 28 from both sides

$\mathbf{2\angle M= 152}$

$\mathbf{\angle M= 76}$

So:

$\mathbf{\angle M= 76}$ and $\mathbf{\angle N= 76}$

3. Triangle EFG

$\mathbf{\angle F+ 23 + 23 = 180}$ --- sum of angles in a triangle

$\mathbf{\angle F+ 46 = 180}$

Subtract 46 from both sides

$\mathbf{\angle F = 134}$

The triangle is an isosceles triangle

So:

$\mathbf{EF = 13}$ and $\mathbf{\angle F = 134}$

4. Triangle PQR

The triangle is an equilateral triangle

So:

$\mathbf{\angle P = \angle Q = \angle R= 60}$

Question 5

The triangle is an isosceles triangle.

So:

$\mathbf{4x + 23 = 10x - 1}$

Collect like terms

$\mathbf{10x - 4x=23+1}$

$\mathbf{6x=24}$

Divide both sides by 6

$\mathbf{x=4}$

Hence, the value of x is 4

Question 6

The triangle is an isosceles triangle.

So:

$\mathbf{9x- 25+9x -25+104 = 180}$

Collect like terms

$\mathbf{9x+9x = 180-104+25+25}$

$\mathbf{18x = 126}$

Divide both sides by 18

$\mathbf{x = 7}$

Hence, the value of x is 7

Question 7

The triangle is an isosceles triangle.

So:

$\mathbf{5x - 7 = 8x - 55}$

Collect like terms

$\mathbf{8x - 5x =55- 7}$

$\mathbf{3x =48}$

Divide both sides by 3

$\mathbf{x =16}$

Hence, the value of x is 16

Question 8

The triangle is an equilateral triangle.

So:

$\mathbf{4x + 8 = 60}$

Subtract 8 from both sides

$\mathbf{4x = 52}$

Divide both sides by 4

$\mathbf{x = 13}$

Hence, the value of x is 13

Read more about triangles at:

https://brainly.com/question/2773823