# Triangle and Rectangle

Pro Problems > Math > Geometry > Triangles## 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.

## Solution

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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?

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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?

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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

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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?

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In the diagram shown,

m ∠DCF = 80

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### Angle Riddle

The angles of a triangle meet the following criteria:

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