Arithmetic AnglesPro Problems > Math > Geometry > Triangles
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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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 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?
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?
If the perimeter of the triangle (in linear units) is equal to the area of the triangle (in square units), what is the length of the side of the square?
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?
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?
Line segment AB is intersected by segment DC, with D on AB, between A and B.
In triangle ADC, m∠ADC = 30º + x and m∠DAC = 50º
In triangle ABC, m∠ACB = 115º + x
In triangle CDB, m∠CDB = 140º + x
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.
In the diagram shown,
m ∠DCF = 80
m ∠ACF = 30
m ∠FBD = 50.
If segment BF bisects ∠ABD, find m ∠BAC.
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
measure of angle ADC = 2y
measure of angle ABD = y
measure of angle ACD = x + y