One of the angles of a triangle is 75 degrees. If the difference of the other two is 35 degrees then the largest angle of the triangle has a measure of_____.

Given:

One of the angles of a triangle is 75 degrees.

The difference of other two is 35 degrees.
To do:

We have to find the measure of the largest angle.

Solution:

Let $ABC$ be the triangle in which $\angle A=75^o$ and $\angle B>\angle C$.
By angle sum property of the triangle,

$\angle A+\angle B+\angle C=180^o$

$75^o+\angle B+\angle C=180^o$

$\angle B+\angle C=180^o-75^o=105^o$......(i)

According to the question,

$\angle B-\angle C=35^o$............(ii)

Adding (i) and (ii), we get,

$\angle B+\angle C+\angle B-\angle C=105^o+35^o$

$2\angle B=140^o$

$\angle B=70^o$

This implies,

$70^o+\angle C=105^o$

$\angle C=105^o-70^o=35^o$

The measure of the largest angle is $75^o$.

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Updated on: 10-Oct-2022

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