Question

chapter 4 test
classify the following triangles by angles and sides by the most precise name.
1)
2)
3)
4)
find the value of the variables
5)
6)
x =
x =
7)
8)
x =
x =
y = 50°
y =
z =

Explanation:

Problem 5

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(x + 63 + 51 = 180\).

Step2: Solve for \(x\)

Simplify: \(x + 114 = 180\). Subtract 114: \(x = 180 - 114 = 66\).

Step1: Identify triangle type (isosceles)

The triangle has two equal sides, so it's isosceles with base angles equal. Let base angles be \(x\).

Step2: Use angle sum

Sum of angles: \(100 + x + x = 180\). Simplify: \(100 + 2x = 180\). Subtract 100: \(2x = 80\). Divide by 2: \(x = 40\).

Step1: Find \(x\) (linear pair)

\(x\) and \(115^\circ\) are linear pair, so \(x = 180 - 115 = 65\).

Step2: Find \(y\) (isosceles triangle)

Triangle is isosceles (two equal sides), so base angles \(x = 65\). Sum of angles: \(y + 65 + 65 = 180\). Simplify: \(y + 130 = 180\). \(y = 50\) (given, but let's confirm).

Step3: Find \(z\) (linear pair with \(x\))

\(z\) and \(x\) are linear pair? Wait, no, \(z\) is equal to \(x\) (vertical or base? Wait, the triangle has two equal sides, so the exterior angle? Wait, \(x = 65\), and \(z\) is equal to \(x\) because the triangle is isosceles, so \(z = 65\)? Wait, no, the base angles are \(x\) and \(z\)? Wait, the triangle has two equal sides, so the base angles are equal. So \(x = z = 65\), and \(y = 50\) (as \(180 - 65 - 65 = 50\)).

Answer:

\(x = 66\)

Problem 6