The correspondence $ABC \leftrightarrow QPR$ between $\Delta ABC$ and $\Delta PQR$ is a similarity. If $m \angle A : m \angle B : m \angle C = 15 : 8 : 7$,find the measures of all the angles of $\Delta PQR$.
(N/A) In $\Delta ABC$,the ratio of the angles is $m \angle A : m \angle B : m \angle C = 15 : 8 : 7$.
Let the angles be $15t$,$8t$,and $7t$ respectively.
Since the sum of angles in a triangle is $180^\circ$,we have $15t + 8t + 7t = 180^\circ$.
$30t = 180^\circ$,which gives $t = 6^\circ$.
Therefore,$m \angle A = 15 \times 6^\circ = 90^\circ$,$m \angle B = 8 \times 6^\circ = 48^\circ$,and $m \angle C = 7 \times 6^\circ = 42^\circ$.
Given the similarity correspondence $ABC \leftrightarrow QPR$,the corresponding angles are equal.
Thus,$m \angle Q = m \angle A = 90^\circ$,$m \angle P = m \angle B = 48^\circ$,and $m \angle R = m \angle C = 42^\circ$.
Hence,the angles of $\Delta PQR$ are $m \angle P = 48^\circ$,$m \angle Q = 90^\circ$,and $m \angle R = 42^\circ$.
Let the angles be $15t$,$8t$,and $7t$ respectively.
Since the sum of angles in a triangle is $180^\circ$,we have $15t + 8t + 7t = 180^\circ$.
$30t = 180^\circ$,which gives $t = 6^\circ$.
Therefore,$m \angle A = 15 \times 6^\circ = 90^\circ$,$m \angle B = 8 \times 6^\circ = 48^\circ$,and $m \angle C = 7 \times 6^\circ = 42^\circ$.
Given the similarity correspondence $ABC \leftrightarrow QPR$,the corresponding angles are equal.
Thus,$m \angle Q = m \angle A = 90^\circ$,$m \angle P = m \angle B = 48^\circ$,and $m \angle R = m \angle C = 42^\circ$.
Hence,the angles of $\Delta PQR$ are $m \angle P = 48^\circ$,$m \angle Q = 90^\circ$,and $m \angle R = 42^\circ$.
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