Triangle VariablesPro Problems > Math > Geometry > Triangles
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?
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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.
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.
In the diagram shown,
m ∠DCF = 80
m ∠ACF = 30
m ∠FBD = 50.
If segment BF bisects ∠ABD, find m ∠BAC.
Two Triangles with Angle Measures
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?
Forty-five and Thirty
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?
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?
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
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?
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?
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