## Angles in a Triangle

## Opening

# Angles in a Triangle

Look at this triangle.

- What do you know about the angles in this triangle?
- Can you use what you know to solve for
*x*?

Look at this triangle.

- What do you know about the angles in this triangle?
- Can you use what you know to solve for
*x*?

Use your knowledge of geometric figures to determine missing angle measures in polygons.

This quadrilateral is a parallelogram.

- What are the measures of ∠
*a*, ∠*b*, and ∠*c*? - Explain how you determined each angle measure.

- What is the sum of the angles in a parallelogram?
- What do you know about opposite angles in a parallelogram?

- What are the measures of ∠
*a*, ∠*b*, ∠*c*, and ∠*d*? - Explain how you determined each angle measure.

- What do you know about vertical angles?
- What do you know about supplementary angles?
- What do you know about the sum of the angles in a triangle?

- Solve for
*x*. - Explain how you solved for
*x*.

- What do you know about the sum of the angles in a triangle?
- What do you know about ∠
*a*?

This quadrilateral is a rhombus.

- Solve for
*x*. - Explain how you solved for
*x*.

- What do you know about the angles in a rhombus?
- What kind of triangle is △
*ABC*? What do you know about the angles in this type of triangle?

- Solve for
*x*. - Explain how you solved for
*x*.

- What do you know about the angles in a pentagon?
- If all of the angles are
*x*degrees, what do you know about the angles?

This figure is a regular pentagon.

- What are the measures of ∠
*a*, ∠*b*, and ∠*c*? - Explain how you determined each angle measure.

What do you know about the angles in a regular pentagon?

- Select two of the previous problems: the one you had the most difficulty with, and the one that was easiest for you. Prepare a presentation about your solutions.
- Be prepared to explain and justify each step of your solutions.

- Imagine a quadrilateral that has two pairs of congruent sides with diagonals that are perpendicular to each other. However, the quadrilateral is not a rhombus. Can you draw this figure?

Take notes about your classmates' strategies and explanations for finding the missing angle measures.

As your classmates present, ask questions such as:

- What do you know about the angles in a parallelogram?
- What is the sum of the angles in a triangle/quadrilateral/pentagon?
- What is true about vertical angles and supplementary angles?
- How did you decide what to do first in order to solve the problem?
- Is there another way to solve the problem?
- What total number of degrees do the
*x*-values represent?

Write a summary about finding missing angle measures in polygons.

Check your summary:

- Do you explain how you can use the relationships of angles in different types of polygons to find missing angles?
- Do you describe some things you know about the angles in different types of polygons?

Complete this Self Check by yourself.

The large figure is a hexagon. Figures *ABGF* and*CDEF* are parallelograms.

- Find the measures of ∠1, ∠2, ∠3, ∠4, and ∠5.
- Explain how you determined each angle measure.
- What is the sum of the angles in the hexagon? How do you know?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**When I look at triangles, quadrilaterals, and other polygons, I see these connections …**