Quadratic Triangle

Pro Problems > Math > Geometry > Triangles

Quadratic Triangle

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?

Presentation mode

Problem by Mr. Twitchell

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

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?

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

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 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.

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,

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?

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?

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 Bisector

In the diagram shown,

m ∠DCF = 80
m ∠ACF = 30
m ∠FBD = 50.

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

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, Three Two-Digit Angle Measures, Triangle and Rectangle, Angle Measure

Blogs on This Site

Book Scrounger

Reviews and book lists - books we love!

Ask Professor Puzzler

The site administrator fields questions from visitors.

Like us on Facebook to get updates about new resources