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:

$\beta =\left(\alpha +\gamma \right)\mathrm{/}2=6{0}^{\circ }$

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
d = 23

Our linear equations calculator calculates it.

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

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:

• Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
• Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
• Sailboat
The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
• Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
• Cuboid
Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
• Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
• Pool
If water flows into the pool by two inlets, fill the whole for 19 hours. The first inlet filled pool 5 hour longer than the second. How long pool take to fill with two inlets separately?
What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13?
• 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?
• Dodecagon
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
• 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 garag
• Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
• n-gon
Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
• Forces
Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
• ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
• Five circles
On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE
• Cone
Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.