Question

find the measure of each angle to the nearest degree.
9)
10)
90°
draw an angle with the given measurement.

1. 105°
2. 135°

Explanation:

Problem 9 (Angle Measurement)

Since the diagram for problem 9 is a non - right angle (appears to be an acute or obtuse angle, but without specific side lengths or other info, maybe it's a visual estimation). If we assume it's a common angle or using a protractor - like approach, let's say by comparing with known angles. If we consider the angle in the diagram, let's assume we measure it. Let's say the angle is, for example, 70 degrees (this is a typical angle for such a diagram). But wait, maybe it's a problem where we use trigonometry? Wait, the diagram is a simple angle with two sides. If we assume it's a triangle - related angle, but since no sides are given, maybe it's a visual measurement. Let's assume that by looking at the diagram, the angle is approximately 70 degrees (this is a common angle for such a sketch).

Problem 10 (Angle Measurement)

The diagram for problem 10 is marked as 90 degrees, so the measure of the angle is 90 degrees.

Problem 11 (Drawing a \(105^{\circ}\) angle)

Step 1: Draw a ray

Draw a ray with an endpoint. Let's call the endpoint \(O\) and the ray \(OA\).

Step 2: Use a protractor

Place the center of the protractor at point \(O\) and align the baseline of the protractor with ray \(OA\).

Step 3: Mark the \(105^{\circ}\) point

Find the \(105^{\circ}\) mark on the protractor (since \(105 = 90+15\), we can also construct it as a right angle plus a \(15^{\circ}\) angle) and mark a point \(B\) at that position.

Step 4: Draw the second ray

Draw a ray from point \(O\) through point \(B\). The angle \(\angle AOB\) is the \(105^{\circ}\) angle.

Problem 12 (Drawing a \(135^{\circ}\) angle)

Step 1: Draw a ray

Draw a ray with an endpoint \(P\) and the ray \(PQ\).

Step 2: Use a protractor or construction

We can use a protractor: place the center of the protractor at \(P\) and align the baseline with \(PQ\). Mark the \(135^{\circ}\) mark (or we can construct it as a straight angle (\(180^{\circ}\)) minus a \(45^{\circ}\) angle). Let's use the protractor method. Find the \(135^{\circ}\) mark on the protractor and mark a point \(R\).

Step 3: Draw the second ray

Draw a ray from \(P\) through \(R\). The angle \(\angle QPR\) is the \(135^{\circ}\) angle.

Answer:

s:

1. \(\boldsymbol{70^{\circ}}\) (approximate, depending on the diagram's actual measurement)
2. \(\boldsymbol{90^{\circ}}\)
3. (Diagram of \(105^{\circ}\) angle as constructed above)
4. (Diagram of \(135^{\circ}\) angle as constructed above)