Question

The measure of the smallest angle of a triangle is 34 less than the measure of the largest angle of the triangle. The measure of the third angle is more than the measure of the smallest angle. Find all three measures .

Answer 1

45degrees, 79egrees and 56degrees

Explanation:

Complete question:

The measure of the smallest angle of a triangle is 34 less than the measure of the largest angle of the triangle. The measure of the third angle is 11 more than the measure of the smallest angle. Find all three measures .

Let the smallest angle be x

Let the largest angle be y

Let the third angle be z

Since the sum of angle in the triangle is 180, then x+y+z = 180 .. 1

If the measure of the smallest angle of a triangle is 34 less than the measure of the largest angle of the triangle, this is expressed as;

x = y - 34

y = x + 34 ..... 2

If the measure of the third angle is 11 more than the measure of the smallest angle, this is expressed as;

z = x + 11 .... 3

Substitute 2 and 3 into 1;

x + (x+34) + (x+11) = 180

x+x+x+45 = 180

3x+45 = 180

3x = 180 - 45

3x = 135

x = 135/3

x = 45 degrees

From 2;

y = x+34

y = 45 + 34

y =79degrees

From3;

z = x+11

z = 45 + 11

z = 56degrees

Hence the measure of the angles are 45degrees, 79egrees and 56degrees