Question

Find mZP in rhombus PQRS.RQ2b-580S2b-98°P

Answer 1

We are given a rhombus figure.

Recall that the consecutive angles in a rhombus add up to 180°

This means that the sum of m∠P and m∠S must be equal to 180°

`m\angle P+m\angle S=180\degree`

Let us substitute the given values into the above equation and solve for b

`\begin{gathered} m\angle P+m\angle S=180 \\ 2b-98+2b-58=180 \\ 2b+2b-98-58=180 \\ 4b-156=180 \\ 4b=180+156 \\ 4b=336 \\ b=(336)/(4) \\ b=84 \end{gathered}`

So, the value of b is 84

Now we can find the angle m∠P

`\begin{gathered} m\angle P=2b-98\degree \\ m\angle P=2(84)-98\degree \\ m\angle P=168\degree-98\degree \\ m\angle P=70\degree \end{gathered}`

Therefore, the value of m∠P is 70°