Question

What do you know to be true about the values of p and g?pºgº6030°4545O A. p>gO B. p

Answer 1

Given the triangles as shown below:

The sum of interior angles in a triangle equals 180°.

Thus, in ΔABC,

`\begin{gathered} \angle A+\angle B+\angle C=180 \\ \text{where} \\ \angle A=60,\text{ }\angle B=p,\text{ }\angle C=30 \\ 60+p+30=180 \\ \Rightarrow p+90=180 \\ p=180-90 \\ \Rightarrow p=90\degree \end{gathered}`

Similarly, in ΔXYZ,

`\begin{gathered} \angle X+\angle Y+\angle Z=180 \\ \text{where} \\ \angle X=45,\text{ }\angle Y=q,\text{ }\angle Z=45 \\ 45+q+45=180 \\ \Rightarrow90+q=180 \\ q=180-90 \\ \therefore q=90\degree \end{gathered}`

Since the p and q are similarly evaluated to be 90°, we can conclude that the values of p and q are equal.

Hence,

`p=q`

The correct option is C.