Question

geometry review topic 2 (# 1 - 18) due 22 (do on separate sheet) ① a b a = b ② c d c + d = 180 ③ 80° 40° x = y = z = ④ 120° x = ⑤ 100 120 x = ⑥ 80 x = y =

Explanation:

Step1: Identify angle - relationship for question 1

Angles a and b are vertical angles. Vertical angles are equal.

Step2: Identify angle - relationship for question 2

Angles c and d are supplementary angles (linear - pair). The sum of supplementary angles is 180 degrees.

Step3: Solve for angles in question 3

For the triangle with 80 - degree angle, using the fact that the sum of angles in a triangle is 180 degrees. Let's assume the third - angle in the first triangle is \(z_1\). So \(z_1=180-(80 + x)\). Also, since the two triangles are related and we know the other non - right angle is 40 degrees. For the second triangle, if we consider the linear - pair and angle - sum properties.
The sum of angles in a triangle is 180 degrees. In the triangle with the 80 - degree angle, if we assume the third angle is \(z_1\), then \(z_1 = 180-(80 + x)\). In the other triangle with the 40 - degree angle, we know that the angles are related by linear - pairs and angle - sum in triangles.
We know that \(x = 60\) (because \(80 + x+40=180\) considering the combined angles of the two - triangle system). Then \(y = 40\) (corresponding angles or alternate interior angles depending on the parallel - line relationship assumed), and \(z = 80\) (corresponding angles).

Step4: Solve for angle in question 4

The 120 - degree angle and x are corresponding angles (assuming parallel lines). Corresponding angles are equal when the lines are parallel. So \(x = 120\).

Step5: Solve for angle in question 5

We use the property of angles formed by intersecting lines. Let's consider the angles around the intersection points. We can find the angle adjacent to 100 degrees is 80 degrees (linear - pair), and the angle adjacent to 120 degrees is 60 degrees (linear - pair). Then, using the angle - sum property for the angles formed by the intersecting lines, \(x = 40\) (by considering the sum of angles around the intersection point).

Step6: Solve for angles in question 6

If we assume the triangle is a right - triangle (from the right - angle symbol), and one angle is 80 degrees. Then \(x = 10\) (since the sum of angles in a triangle is 180 degrees, \(x=180-(90 + 80)\)). And \(y = 100\) (linear - pair with the 80 - degree angle).

Answer:

1. Vertical angles are equal
2. Supplementary angles (linear - pair)
3. \(x = 60\), \(y = 40\), \(z = 80\)
4. \(x = 120\)
5. \(x = 40\)
6. \(x = 10\), \(y = 100\)