Question

geometry
name_
isosceles and equilateral triangle practice
date_
find the value of x.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: Use the property of isosceles triangle (1)

In an isosceles triangle, the base angles are equal. So \(x = 70^{\circ}\)

Step2: Use the property of equilateral triangle (2)

Since all sides are equal, it is an equilateral triangle. All angles are \(60^{\circ}\), so \(x=60^{\circ}\)

Step3: Use the property of isosceles triangle (3)

In an isosceles triangle, the base angles are equal. The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(y\), \(y = 72^{\circ}\), \(x=\frac{180 - 72}{2}=54^{\circ}\)

Step4: Use the property of right - isosceles triangle (4)

In a right - isosceles triangle (assuming the mark indicates equal sides), the sum of angles is \(180^{\circ}\), \(x = 90 - 43=47^{\circ}\)

Step5: Use the exterior angle property (5)

In an isosceles triangle, the base angles are equal. Let the base angles be \(x\), using the exterior angle property (exterior angle = sum of two non - adjacent interior angles). But if we assume it's an isosceles triangle, \(x = 27^{\circ}\)

Step6: Use the exterior angle property (6)

In an isosceles triangle, the base angles are equal. The exterior angle \(x=70^{\circ}\) (exterior angle of an isosceles triangle with base angles equal)

Step7: Use the property of isosceles triangle (7)

Since two sides are equal (assuming the marks), the base angles are equal. But without more information (if it's a triangle with side lengths, assuming it's an isosceles triangle in terms of angles, but if we assume it's a triangle with side \(10\) and \(x\) (assuming \(x = 10\) as sides of an isosceles triangle)

Step8: Use the property of right - isosceles triangle (8)

In a right - isosceles triangle (assuming the right angle and equal sides mark), the two non - right angles are equal. Let the right angle be \(90^{\circ}\), \(x = 45^{\circ}\)

Answer:

1. \(70^{\circ}\)
2. \(60^{\circ}\)
3. \(54^{\circ}\)
4. \(47^{\circ}\)
5. \(27^{\circ}\)
6. \(70^{\circ}\)
7. \(10\) (assuming side length equality)
8. \(45^{\circ}\)