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Finding angle measures 2
Description
Exercise Name: Finding angle measures 2
Math Missions: 8th grade (U.S.) Math Mission, High school geometry Math Mission
Types of Problems: 2

The Finding angle measures 2 exercise appears under the 8th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise uses several facts about the angles to practice finding missing angles in geometric diagrams.

## Types of Problems

There are two types of problems in this exercise:

1. Find the labeled angle in the star: This problem provides a five-point star and a missing angle. The user is asked to use various facts about angles to find the measure of the missing angle.
2. Use the transversal diagram to find a particular angle: This problem provides a standard transversal diagram with some information and a missing angle. The user is expected to use the angle facts to find the missing angle.

## Strategies

Knowledge and comfort with the angle theorems are instrumental to doing this exercise correctly.

1. In triangles the sum of all angles in a triangle is ${180^\circ}$ and the measure of an exterior angle is equal to the sum of the two remote interior angles. In the problem with the star the answer boils down to one of these facts.
2. With transversals and parallel lines, alternate interior angles, corresponding angles, and alternate interior angles are congruent. Additionally, same-side interior and exterior angles are supplementary.
3. With intersecting lines vertical angles are congruent, perpendicular lines form right angles, and the sum of the angles in a line is ${180^\circ}$.

## Real-life Applications

1. Geometric concepts, such as the ones used in this exercise, are instrumental in architecture (drafting), art and graphical design.
2. Geometry is important for computer aided design.
3. Engineers and architects use angles for designs, roads, buildings and sporting facilities.
4. Athletes use angles to enhance their performance. Carpenters use angles to make chairs, tables and sofas.
5. Artists use their knowledge of angles to sketch portraits and paintings.