Question 1

Sam, a self-confessed math geek, is mowing his four-sided yard. He is really bored so he tries to remember all of its dimensions. He remembers that one corner is 85°, another is 70°, and another is 105°, but he can’t recall the 4th, so he has to calculate it. Figure out the measure of the fourth corner with him.

Question 2

ANSWER:

100°

Explanation:

Since you want to form a 4-sided figure, the sum of all the vertex angles must be 360°.

Therefore, we can calculate the 4th vertex, like this:

$\begin{gathered} \measuredangle1+\measuredangle2+\operatorname{\measuredangle}3+\operatorname{\measuredangle}4=360\degree \\ \\ \operatorname{\measuredangle}4=360\degree-\measuredangle1-\measuredangle2-\measuredangle3 \\ \\ \text{ We replacing:} \\ \\ \operatorname{\measuredangle}4=360\degree-85\degree-70\degree-105\degree \\ \\ \operatorname{\measuredangle}4=100\degree \end{gathered}$

So the measure of the fourth corner is 100°

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