Given:
Two triangles congruent by ASA.
To find:
The the measures of x, y, angle QPR and angle QRP.
Solution:
The triangles PQR and PSR are congruent by ASA. So,
[tex]\angle QPR\cong \angle SPR[/tex]
[tex]PR\cong PR[/tex]
[tex]\angle QRP\cong \angle SRP[/tex]
Now,
[tex]m\angle QPR=m\angle SPR[/tex]
[tex]2x+1=x+18[/tex]
[tex]2x-x=18-1[/tex]
[tex]x=17[/tex]
And,
[tex]\angle QRP= \angle SRP[/tex]
[tex]8y-4=4y+28[/tex]
[tex]8y-4y=4+28[/tex]
[tex]4y=32[/tex]
Divide both sides by 4.
[tex]y=8[/tex]
The measure of angle QPR is:
[tex]m\angle QPR=(2x+1)^\circ[/tex]
[tex]m\angle QPR=(2(17)+1)^\circ[/tex]
[tex]m\angle QPR=(35+1)^\circ[/tex]
[tex]m\angle QPR=36^\circ[/tex]
And,
[tex]m\angle QRP=(8y-4)^\circ[/tex]
[tex]m\angle QRP=(8(8)-4)^\circ[/tex]
[tex]m\angle QRP=(64-4)^\circ[/tex]
[tex]m\angle QRP=60^\circ[/tex]
Therefore, the required values are [tex]x=17, y=8, m\angle QPR=36^\circ ,m\angle QRP=60^\circ[/tex].
