Chapter CSB1.9, Problem 6E

To determine

The angle $\angle XZT$ first by estimation, then using a protractor and finally classify the angle as acute, obtuse, right or straight.

Answer to Problem 6E

Estimated measure: 135°

Actual measure: 133°

Classification: Obtuse

Explanation of Solution

Given information:

Following figure is given:

  

From the figure it can be seen that $\angle UZX\approx 90°$ and $\angle TZU\approx 45°$ .

Also $\angle XZT=\angle TZU+\angle UZX$ .Therefore, $\angle XZT\approx 90+45=135°$ .

To actually measure angle $\angle XZT$ performing following steps:

Step 1:

Place the center point of the protractor’s base on vertex D. Align the straight side with $\overrightarrow{DE}$ so the marker for 0° is one of the rays

Step 2:

Use the scale that begins with 0° at $\overrightarrow{DE}$ . Read where the other side of the angle, $\overrightarrow{DC}$ , crosses this scale.

The angle measure is shown below:

  

Since the angle is larger than 90°, hence it is an obtuse angle.