# 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 result:

α =  37 °
β =  60 °

#### Solution:

$\alpha+\beta+\gamma = 180 \ \\ \beta = \alpha + d \ \\ \gamma = 83 ^\circ = \alpha + 2d \ \\ \ \\ 3 \alpha + 3d = 180 \ \\ 2 \alpha + d = 180 - \gamma = 23 ^\circ \ \\ \ \\ 3 \alpha + 3d = 180 \ \\ 2 \alpha + 2d = 23 \ \\ \ \\ \alpha = 37 ^\circ$
$\beta = (\alpha + \gamma)/2 = 60 ^\circ$

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

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

Calculated by our linear equations calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Looking for help with calculating arithmetic mean?
Looking for a statistical calculator?
Do you have a system of equations and looking for calculator system of linear equations?

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

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

## Next similar math problems:

• Six-sided polygon
In a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.
• Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
• Largest angle of the triangle
What is the largest angle of the triangle if the second angle is 10° greater than twice the first and the third is 30° smaller than the second?
• The second
The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
• The tower
The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
• Three parallels
The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
• Triangle 42
Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
• Angle at the apex
In an isosceles triangle, the angle at the apex is 30° greater than the angle at the base. How big are the internal angles?
• In a 2
In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
• Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
• A triangle
A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
• Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
• Inscribed circle
Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
• Trapezium internal angles
A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.
• Garage
There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the gara
• Supplementary angles
One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
• Vector v4
Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1)