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

What is the measurement of Angle D?

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

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    $\begingroup$ it is equal to 45 $\endgroup$ – Kelly May 16 at 18:47
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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, $\angle D = 180^\circ - \angle DBC - \angle BCD = 180^\circ -(90^\circ - \frac{\beta}{2}) - \beta - \frac{\alpha}{2} = 90^\circ - \frac{\beta}{2} - \frac{\alpha}{2}= 45^\circ$

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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.

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