Question

independent practice: isosceles & equilateral triangles

1. ( x = ) find the value of ( x ).

1. ( x = ) find the value of ( x ).

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the base - angles are equal. Also, the sum of angles in a triangle is \(180^{\circ}\).
For problem 5:
Let the two equal angles be \(x\) (the base - angles). We know that \(x + x+110^{\circ}=180^{\circ}\)

Step2: Solve the equation for \(x\) in problem 5

Combine like terms: \(2x=180^{\circ}- 110^{\circ}\)
\(2x = 70^{\circ}\)
Divide both sides by 2: \(x=\frac{70^{\circ}}{2}=35^{\circ}\)

For problem 6:
Since two sides are equal (lengths 6 and 6), the triangle is isosceles. Let the angles opposite to the equal sides be equal. Let the unknown angle be \(x\). We know that \(x + 59^{\circ}+y = 180^{\circ}\), and since the sides of length 6 are equal, the angles opposite to them (\(x\) and \(y\)) are equal. But wait, no, if two sides are 6 (and the third side is 6.2), the angles opposite to the sides of length 6 are equal. So \(x\) is opposite to a side of length 6 and the other angle opposite to the side of length 6 is also \(x\). Using the angle - sum property of a triangle \(x + x+59^{\circ}=180^{\circ}\) (wait no, wrong, if two sides are 6, then the angles opposite to them are equal. So \(x\) is one of them. \(x + 59^{\circ}+z=180^{\circ}\), but if two sides are 6, then \(x = z\) (angles opposite to equal sides). So \(2x+59^{\circ}=180^{\circ}\)
\(2x=180^{\circ}-59^{\circ}=121^{\circ}\)
\(x = 60.5^{\circ}\)

Answer:

1. \(35\)
2. \(60.5\)