Triangle Variables

Pro Problems > Math > Geometry > Triangles

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?

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 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.

Angle Bisector

In the diagram shown,

m ∠DCF = 80
m ∠ACF = 30
m ∠FBD = 50.

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

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?

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?

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?

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.

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?

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?