thagem01 wrote:

Hi Guys,

Please find attached a question of geometry that i do not understand.

Could you please give me the explanation?

Thanks

Neither (1) nor (2) alone is sufficient.

Let's see why together they are sufficient:

(1) and (2) together: Triangle RQS isosceles, so \(\angle {RSQ}=\frac{180^o-\angle{R}}{2}\).

Similarly, triangle TSU is asosceles, so \(\angle{TSU}=\frac{180^o-\angle{T}}{2}\).

It follows that \(x=180-90+\frac{\angle{R}}{2}-90+\frac{\angle{T}}{2}=\frac{\angle{R}+\angle{T}}{2}=\frac{90}{2}=45\), because triangle PRT is right angled.

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