# Angle Bisector

Pro Problems > Math > Geometry > Triangles## Angle Bisector

In the diagram shown,

m ∠DCF = 80

m ∠ACF = 30

m ∠FBD = 50.

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

## 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

### 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?

### Triangle and Rectangle

In the diagram displayed, the triangle splits the rectangle into three similar triangles. Find the value of AD^{2} divided by the product of DE and EC.

### 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?

### 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?

### Angle Riddle

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.

### Three Two-Digit Angle Measures

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?

### 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 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?

### 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.

### 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?