Question

In triangle abc the measure of angle a is 5 degrees more that 3 times the measure of angle b . angle c measures 20 degrees less than angle B . determine the measures of angle a b and c

Answer 1

a = 122°, b = 39° and c = 19°

angle a = 3b + 5 and angle c = b - 20

The sum of the angles in a triangle = 180°

Thus 3b + 5 + b + b - 20 = 180 ( solve for b)

5b - 15 = 180

add 15 to both sides

5b = 180 + 15 = 195

divide both sides by 5

b = $\frac{195}{5}$ = 39

angles are a = ( 3 × 39) + 5 = 122°, b = 39°, c = 39 - 20 = 19°

Answer 2

Measures of angles $a,b,c$ are equal to $122^{\circ},39^{\circ},19^{\circ}$ respectively.

According to the angle sum property of a triangle, sum of all the angles of a triangle is equal to $\boldsymbol{180^{\circ}}$

Let measure of angle $b$ be $x$

Measure of angle $a=5+3x$

Measure of angle $c=x-20$

So,

$5+3x+x+x-20=180^{\circ}$

                           $5x=195$

                             $x=39$

Measure of angle $a=5+3(39)$

                                 $=122^{\circ}$

Measure of angle $b=39^{\circ}$

Measure of angle $c=39-20$

                                $=19^{\circ}$

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