Question

17. If m angle 1 = 27, and m angle 2 = 24, find the measure of arc AB18. If m angle 3 = 58, and m angle 4 = 56, find the measure of arc BC

Answer 1

Question 17:

Let us redraw the question given with the information given in the question.

The value of the measure of the arc AB is labelled as x degrees. We will apply the angle sum theorem of a triangle to solve this question.

`\begin{gathered} Angle\text{ sum theorem of a triangle:} \\ \text{The sum of angles in a triangle is }180^0 \\ \\ \text{Thus, we can write that:} \\ 27^0+24^0+x^0=180^0 \\ 51^0+x=180^0 \\ \text{Subtract }51^0\text{ from both sides} \\ \\ x=180^0-51^0=129^0 \end{gathered}`

Question 18:

Let us redraw the circle as follows:

Applying the angle sum theorem of a triangle once more, we have: