Question

One of the angles of a triangle is ${75}^{\circ }$. If the difference of the other two angles is ${35}^{\circ }$, then the largest angle of the triangle has a measure of :

• A. ${80}^{\circ }$
• B. ${75}^{\circ }$
• C. ${100}^{\circ }$
• D. ${135}^{\circ }$

Answer 1

Answer: (B)

${75}^{\circ }$

Let the other two angles be $x$ and $y$

Given $x-y={35}^{\circ }...........\left(i\right)$

Now using angle sum property of triangle

$\Rightarrow x+y{+75}^{\circ }={180}^{\circ }\Rightarrow x+y={105}^{\circ }...........\left(ii\right)$

Solving $\left(i\right)$ and $\left(ii\right)$

$x={70}^{\circ },y={35}^{\circ }$

So the measure of largest angle is ${75}^{\circ }$