# Arithmetic Angles

Pro Problems > Math > Geometry > Triangles## Arithmetic Angles

The angles of a triangle are in arithmetic progression, and the difference between the largest and smallest angle is 42 degrees. What are the three angles?

## Solution

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The angles of a triangle meet the following criteria:

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- Exactly two of my angle measures are palindromic.
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Two of the angles of a triangle are 45 degrees and 30 degrees. The altitude from the third angle has length 15 units. What is the triangle's area?

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In the diagram shown,

m ∠DCF = 80

m ∠ACF = 30

m ∠FBD = 50.

If segment BF bisects ∠ABD, find m ∠BAC.

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Triangle ABC is inside square ABDE, and C lies along side DE. If the area of the triangle is 24 square units, what is the length of AB?

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Segment AD is drawn in triangle ABC, with D on side BC. Given the following information, determine the measure of angle ADB.

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Line segment AB is intersected by segment DC, with D on AB, between A and B.

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The angles in a triangle have measures x, x + 10, and y.

The angles in a second triangle have measures x + y, 40, and 50.

The angles in a third triangle have measures x – y, 40, and z.

What is the value of z?

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In a triangle, the measure of the largest angle is 12 less than the sum of the measures of the other two angles. The largest angle is also 52 more than the twice the middle angle decreased by three times the smallest angle. What is the largest angle measure?