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# 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?

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Problem by Mr. Twitchell

## Solution

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## Similar Problems

### Three Triangles

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?

### Triangle in a Square

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?

### Quadratic Triangle

The angles in a triangle have measures x2 - 5, 2x + 18, and x + 37. What is the measure of the largest angle in the triangle?

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A triangle is placed on the interior of a square so that two of the triangle's vertices lie on two adjacent vertices of the square, and the third vertex lies on the opposite side,
1
3
of the way between the two endpoints.

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### Three Two-Digit Angle Measures

The measures of the angles in a triangle are all two digit numbers, and two of them end in 3. Exactly two of them contain the digit 4. None of the angle measures are multiples of three. What are the measures of the angles?

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An isosceles triangle is a triangle in which two of the angles have the same measure. In an isosceles triangle, the angle measures are 30 + x, 62 - x, and 10 + 2x + y. What are the possible numeric values for the measures of the angles?

### Angle Measure

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In triangle ABC, m∠ACB = 115º + x

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Find m∠CBD.

### Triangle and Rectangle

In the diagram displayed, the triangle splits the rectangle into three similar triangles. Find the value of AD2 divided by the product of DE and EC.

### Angle Bisector

In the diagram shown,

m ∠DCF = 80
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If segment BF bisects  ∠ABD, find m ∠BAC.

### Split Triangle

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

measure of angle BAD = x
measure of angle CAD = 2x
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Angle Riddle, Two Triangles with Angle Measures, Angles in a Triangle, Forty-five and Thirty

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