Question

A quadrilateral has two angles that measure 300° and 25º. The other two angles are in aratio of 3:4. What are the measures of those two angles?andoSubmit

Answer 1

Hello!

First, we must remember that the sum of the four internal angles of a quadrilateral must be 360º.

Knowing it, let's analyze your exercise:

Notice that we already know two angles:

`300º+25º=325º`

So, we can discover how many angles are left to complete 360º, look:

`360º-325º=35º`

I will call the missing angles A and B, okay?

At this moment, we know that:

`A+B=35\degree`

The exercise informs us that these angles are in a ratio of 3:4. We can write it as:

`\begin{gathered} 3x+4x=35 \\ 7x=35 \\ x=(35)/(7) \\ x=5 \end{gathered}`

As we know the value of X, we can obtain the missing angles:

`\begin{gathered} A=3\cdot x \\ A=3\cdot5 \\ A=15 \\ \\ B=4\cdot x \\ B=4\cdot5 \\ B=20 \end{gathered}`What are the measures of those two angles?

Answer: 15 and 20.