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OverLord2011 [107]
2 years ago
5

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 a

s large as the smallest angle. Find the measures of all three angles.
Mathematics
1 answer:
umka21 [38]2 years ago
4 0

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\°

<em>Find the value of x</em>

x=y+100  ---- x=20+100=120\°

<em>Find the value of z</em>

z=2y ----> z=2(20)=40\°

therefore

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

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