Question

Here are two patterns made using identical rhombuses. Write one equation to show how to find the value of ​a​ and one equation to show how to find the value of ​b​. Then find both values.

Equation 1​ ________________________________________
Equation 2​ ________________________________________
Answer​ ​a​ = _________________________ and ​b​ = _________________________

Answer 1

Equation 1​

6*a = 360°

Equation 2

2*a + 2*b = 360°

a = 60°

b = 120°

Explanation:

From the first picture we can see that 6 angles a° made a complete circle, that is, 360°. So:

6*a = 360°

a = 360°/6 = 60°

From the second picture we can see that 2 angles a° and 2 angles b° made a complete circle, then:

2*a + 2*b = 360°

2*b = 360° - 2*60°

b = 240°/2 = 120°