Question

Here are two patterns made using identical rhombuses. Without using a protractor, determine the value of a and b.

Answer 1

a = 60°

b = 120°

Explanation:

First, you can find measure a by using the first shape. There are six rhombuses, and you can use the innermost a of each one to form a circle. A full circle is 360°, so divide 360 by six. The answer is sixty. So on the next shape, the a measurements add up to 120°. Subtract that from the circle: 360 - 120 = 240. And since there are two measurements for b, you would divide 240 by two. The answer is 120.

To check your work, use the knowledge that circles are 360° (the four interior corners of a rhombus will also add up to 360°. 2(120) + 2(60) = 360. Hope this helps! Feel free to ask any questions!