# What is measurement of angle D? [closed]

Angle 1= Angle 2, Angle 3 = Angle 4, Angle A = 90º

What is the measurement of Angle D?

## closed as off-topic by Moishe Kohan, kjetil b halvorsen, YuiTo Cheng, Adrian Keister, Xander HendersonMay 17 at 17:45

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• it is equal to 45 – Kelly May 16 at 18:47

## 2 Answers

Let $$\angle ABC=\beta, \angle BCA = \alpha$$, note that $$\alpha + \beta = 90^\circ$$

Now, $$\angle3 = \frac{180^\circ -\beta}{2}$$ and $$\angle 2 = \frac{\alpha}{2}$$

So, $$\angle D = 180^\circ - \angle DBC - \angle BCD = 180^\circ -(90^\circ - \frac{\beta}{2}) - \beta - \frac{\alpha}{2} = 90^\circ - \frac{\beta}{2} - \frac{\alpha}{2}= 45^\circ$$

Angle chasing. Each of $$(1,2,3,4)$$ is 45 deg due to bisection. Due to the isosceles right triangle $$BAC, \angle ABC$$ also measures 45 deg. When three out of four angles each 45 deg is accounted for, what remains at D is 45 deg.