We want to find the measure of ∠ Q from the following diagram.
First, recall that the sum of measures of angles around the point equals 360^(∘).
Let's use this fact to find the measure of the reflexive angle that is adjacent to the obtuse ∠ PSR.
360^(∘) - 140^(∘) = 220^(∘)
Let's add this measure to the given diagram. Now, let's focus on the interior angles of a quadrilateral Q P S R.
In a quadrilateral, the sum of interior angles equals 360^(∘). We can use this fact for quadrilateral Q P S R in order to write an equation for m ∠ Q.
m ∠ Q+ 40^(∘) + 220^(∘) + 35^(∘) = 360^(∘)
Finally, let's solve this equation!
