Question

The angles in a triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times as large as the smallest angle. Find the measures of all three angles.

Answer 1

Answer:

The measure of the three angles are 120°, 20° and 40°

Step-by-step explanation:

Let

x ----> the measure of the first angle

y ---> the measure of the second angle (smallest angle)

z ---> the measure of the third angle

Remember that

The sum of the angles in a triangle must be equal to 180 degrees

so

$x+y+z=180$ ----> equation A

$x=y+100$ -----> equation B

$z=2y$ ------> equation C

solve the system by substitution

substitute equation B and equation C in equation A

$(y+100)+y+(2y)=180$

solve for y

$4y+100=180$

$4y=180-100$

$4y=80$

$y=20\°$

Find the value of x

$x=y+100$  ---- $x=20+100=120\°$

Find the value of z

$z=2y$ ----> $z=2(20)=40\°$

therefore

The measure of the three angles are 120°, 20° and 40°