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?

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?

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?

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?

In a triangle, the angles measures are: 3x + 44, x, and 2x - 20. In a second triangle, two of the angle measures are x + 20 and 2x - 5. What is the measure of the third angle?

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?

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 of a triangle meet the following criteria:

• All the angle measures are prime numbers.
• All the angle measures are distinct.
• Exactly two of my angle measures are palindromic.
• The difference between my two largest angle measures is a two digit number x.
• One of the digits of x is twice the other digit.

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

In the diagram shown,

m ∠DCF = 80
m ∠ACF = 30
m ∠FBD = 50.

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