Question

Can you please help me out with a question

Answer 1

Therefore, the answer is option B.

Answer 2

From Thales's theorem, which states that in a inscribed triangle, where its hypotenuse its the diameter of a circle, its angle opposite to the hypotenuse is a right angle, so we get

`(2x+9)+90+(4x-3)=180`

because interior angles of a triangle add up to 180 degrees. By combining similar terms, from our last relation, we get

`\begin{gathered} 2x+4x+9-3+90=180 \\ 6x+6+90=180 \\ 6x+96=180 \end{gathered}`

By moving 96 to the right hand side, we have

`\begin{gathered} 6x=180-96 \\ 6x=84 \end{gathered}`

Then, x is given by

`\begin{gathered} x=(84)/(6) \\ x=14 \end{gathered}`

Therefore, the answer is option B.