In a triangle, the measure of the middle angle is triple the measure of the smallest angle, and
the measure of the largest angle is 55° greater
than the measure of the smallest angle. Find
the measures of the
angles.

We have that the measures of the  angles are as follows

From the question we are told that:

The measure of the middle angle  is triple the measure of the smallest angle

The measure of the largest angle is 55° greater  than the measure of the smallest angle

Let

Therefore

Generally, the equation for the angle of a triangle is mathematically given by

Therefore

Therefore

Substitute into equations of and

For

For

in conclusion

The measures of the  angles are as follows

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Let the smallest angle in a triangle be = x

Largest angle in a triangle = 55 + x

The middle angle in a triangle = 3x ( triple the measure of the smallest angle )

Their sum = 180° ( according to the angle sum property all the angles of a triangle sum up to 180° )

This can be written as :

= x + 55 + × + 3x = 180

Let us find each angle by solving the equation .

= x + 55 + x + 3x = 180°

= x + x + 3x + 55 = 180°

= 5x + 55 = 180°

= 5x = 180 - 55 ( transposing +55 from LHS to RHS changes +55 to -55 )

= 5x = 125

= x = 125 ÷ 5 (transposing ×5 from LHS to RHS changes ×5 to ÷5 )

= x = 25

Using this let us find the measure of each angle .

Smallest angle = x = 25

Smallest angle = 25°

Middle angle = 3x = 3 × 25 = 75

Middle angle = 75°

The largest angle = x + 55 = 25 + 55 = 80

Largest angle = 80°

Therefore , the measure of the smallest angle = 25° , the measure of the middle angle = 75° and the measure of the largest angle = 80° .

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