Show angle CAB is the same size as angle EAD

Question

Let A = (0,0), B = (1,2), C = (6,2), D = (2,−1), and E = (1,−3).

Show that angle CAB is the same size as angle EAD.

Answer 1

Slope of AC: m_AC = (2 - 0)/(6 - 0) = 1/3; Slope of AB: m_AB = (2 - 0)/(1 - 0) = 2;

tanCAB = (2 - 1/3)/(1 + 2·1/3) = 1. So angle CAB = 45°..

Slope AE: m_AE = (- 3 - 0)/(1 - 0) = - 3; slope AD: m_AD = (- 1 - 0)/(2 - 0) = = - 1/2.

So, tanEAD = (-1/2 + 3)/(1 + 3/2) = 1. So, angle EAD = angle CAB = 45°

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Answer 2

What are the measure of the following?∠

∠BAD and ∠CAE

Use Angle Addition (subtraction)