Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°.

What sizes have other angles in a triangle?

Correct answer:

α =  37 °
β =  60 °

Step-by-step explanation:


a+b+c = 180;b = a + d; c = a + 2d;c = 83

a+b+c = 180
b = a + d
c = a + 2·d
c = 83

a+b+c = 180
a-b+d = 0
a-c+2d = 0
c = 83

Row 2 - Row 1 → Row 2
a+b+c = 180
-2b-c+d = -180
a-c+2d = 0
c = 83

Row 3 - Row 1 → Row 3
a+b+c = 180
-2b-c+d = -180
-b-2c+2d = -180
c = 83

Row 3 - -1/-2 · Row 2 → Row 3
a+b+c = 180
-2b-c+d = -180
-1.5c+1.5d = -90
c = 83

Row 4 - 1/-1.5 · Row 3 → Row 4
a+b+c = 180
-2b-c+d = -180
-1.5c+1.5d = -90
d = 23


d = 23/1 = 23
c = -90-1.5d/-1.5 = -90-1.5 · 23/-1.5 = 83
b = -180+c-d/-2 = -180+83-23/-2 = 60
a = 180-b-c = 180-60-83 = 37

a = 37
b = 60
c = 83
d = 23

Our linear equations calculator calculates it.

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Looking for help with calculating arithmetic mean?
Looking for a statistical calculator?
Do you have a system of equations and are looking for calculator system of linear equations?
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: