Games
Problems
Go Pro!

Split Triangle

Pro Problems > Math > Geometry > Triangles
 

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

Presentation mode
Problem by BogusBoy

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.
Assign this problem
Click here to assign this problem to your students.

Similar Problems

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?

Angle Bisector

In the diagram shown,

m ∠DCF = 80
m ∠ACF = 30
m ∠FBD = 50.

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

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.

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?

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?

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?

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?

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?

Triangle in a Square

A triangle is placed on the interior of a square so that two of the triangle's vertices lie on two adjacent vertices of the square, and the third vertex lies on the opposite side,
1
3
of the way between the two endpoints.

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 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.
Angle Measure, Triangle Variables, Three Two-Digit Angle Measures, Quadratic Triangle

Understanding Coronavirus Spread

A Question and Answer session with Professor Puzzler about the math behind infection spread.

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy