Question:
<p>In<span class="math-tex">\(\triangle\)</span>ABC, if <span class="math-tex">\(\angle\)</span>C = 50° and <span class="math-tex">\(\angle\)</span>A exceeds <span class="math-tex">\(\angle\)</span>B by 44<sup>o</sup>, then <span class="math-tex">\(\angle\)</span>A =</p>
<p style="display:inline">40<sup>o</sup></p>
<p style="display:inline">43<sup>o</sup></p>
<p style="display:inline">67<sup>o</sup></p>
<p style="display:inline">87<sup>o</sup></p>
Step-by-Step Solution
Key Concept: Apply the angle sum property of triangles to form a system of linear equations based on the given relationships between the angles.
<p>Let x and y be the measures of <span class="math-tex">$\angle$</span>A and <span class="math-tex">$\angle$</span>B respectively.<br />
Now,<span class="math-tex">$\angle$</span>A +<span class="math-tex">$\angle$</span>B +<span class="math-tex">$\angle$</span>C = 18<sup>o</sup>[By angle sum property]<br />
<span class="math-tex">$\Rightarrow$</span>x + y + 50<sup>o</sup> = 180<sup>o</sup>[Given,<span class="math-tex">$\angle$</span>C = 50<sup>o</sup>]<br />
<span class="math-tex">$\Rightarrow$</span>x + y = 130<sup>o</sup> ...(i)<br />
Also,<span class="math-tex">$\angle$</span>A -<span class="math-tex">$\angle$</span>B = 44<sup>o</sup><span class="math-tex">$\Rightarrow$</span>x - y = 44<sup>o</sup> ...(ii)<br />
Adding (i) and (ii), we get<br />
2x = 174<sup>o</sup><span class="math-tex">$\Rightarrow$</span>x = 87<sup>o</sup><span class="math-tex">$\Rightarrow$</span><span class="math-tex">$\angle$</span>A = 87<sup>o</sup></p>
Correct Answer: D