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$$\angle P$$ is $$15^\circ$$ greater than $$\frac{5}{9}$$ times the difference of a right angle and its half. Type of $$\angle P$$ is
The difference of a right angle and its half is $$90^\circ - 45^\circ = 45^\circ$$. Then $$\frac{5}{9} \times 45^\circ = 25^\circ$$, so $$\angle P = 25^\circ + 15^\circ = 40^\circ$$. Since it is less than $$90^\circ$$, $$\angle P$$ is an acute angle.
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