# Three Triangles

Pro Problems > Math > Geometry > Triangles## 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?

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.## Similar Problems

### 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

measure of angle ADC = 2y

measure of angle ABD = y

measure of angle ACD = x + y

### Triangle in a Square

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?

### Angles in a Triangle

In a triangle, the measure of the largest angle is 12 less than the sum of the measures of the other two angles. The largest angle is also 52 more than the twice the middle angle decreased by three times the smallest angle. What is the largest angle measure?

### 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?

### Quadratic Triangle

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

### Angle Bisector

In the diagram shown,

m ∠DCF = 80

m ∠ACF = 30

m ∠FBD = 50.

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

### 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?

### Triangle Variables

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?

### 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?

### Angle Measure

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

Find m∠CBD.