Forty-five and ThirtyPro Problems > Math > Geometry > Triangles
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?
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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?
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.
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?
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.
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?
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?