Question:
<p>The angles of a triangle are x<sup>o</sup>, y<sup>o</sup> and 40<sup>o</sup>. The difference between the two angles x and y is 30<sup>o</sup>, then</p>
<p style="display:inline">x<sup>o</sup> = 85<sup>o</sup> and y<sup>o</sup> = 55<sup>o</sup></p>
<p style="display:inline">x<sup>o</sup> = 95<sup>o</sup> and y<sup>o</sup> = 35<sup>o</sup></p>
<p style="display:inline">x<sup>o</sup> = 75<sup>o</sup> and y<sup>o</sup> = 45<sup>o</sup></p>
<p style="display:inline">x<sup>o</sup> = 65<sup>o</sup> and y<sup>o</sup> = 95<sup>o</sup></p>
Step-by-Step Solution
Key Concept: Utilize the angle sum property of a triangle to determine the sum of the unknown angles and solve the resulting system of linear equations using the given difference.
<p>According to the question,<br />
x<sup>o</sup> + y<sup>o</sup> + 40<sup>o</sup> = 180<sup>o</sup><br />
x<sup>o</sup> + y<sup>o</sup> = 140<sup>o</sup> ... (i)<br />
and x<sup>o</sup> + y<sup>o</sup> = 30<sup>o</sup> ... (ii)<br />
and y<sup>o</sup> = 55<sup>o</sup><br />
On solving eq. (i) and eq. (ii),<br />
x + y + x - y = 140 + 30<br />
2x = 170<br />
x = 85<sup>o</sup><br />
Putting the value of x in equation (i), we get<br />
85<sup>o</sup> + y = 140<sup>o</sup><br />
y = 140<sup>o</sup> - 85<sup>o</sup><br />
y = 55<sup>o</sup><br />
we get x<sup>o</sup> = 85<sup>o</sup> and y<sup>o</sup> = 55<sup>o</sup></p>
Correct Answer: A