# 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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Segment AD is drawn in triangle ABC, with D on side BC. Given the following information, determine the measure of angle ADB.

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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.