Question

How do I find the missing angles mark by letters in these parallelograms?

Answer 1

A parallelogram is a geometrical shape such that its adjacent angles are supplementary, in other words, the addition of two angles that are next to one another is equal to 180°.

In the figure, b is next to c, b is next to a and a is next to the 30° angle; therefore:

`\begin{gathered} b+c=180 \\ b+a=180 \\ a+30=180 \end{gathered}`

We have a system of three equations and three unknowns, we can solve it as follows:

`\begin{gathered} a+30=180 \\ \Rightarrow a=150 \\ b+a=180 \\ \Rightarrow b=180-a \\ \Rightarrow b=30 \\ b+c=180 \\ \Rightarrow c=180-b \\ \Rightarrow c=150 \end{gathered}`

Thus, the answers are a=150°, b=30°, c=150°