Question

In the given square ABCD, find the measure of angle DAC.

I want the answer step by step​

Answer 1

$\underline{ \LARGE \textsf{ \textbf{ \red{Required Solution}}}}$

As we know in a square every angle is equal to 90°.

Now in ∆ACD,

$\textsf { \textbf{AD = CD (all sides of a square are equal)}}$

We know angle opposite to equal sides are equal so

We know sum of all angles of a triangle is equal to 180°

$\angle \textsf{ \textbf{1= }} \angle \textsf{ \textbf{2=x (say)}}$

$\sf \angle1+\angle2+\angle D = 180° \\ \sf x+x+90\degree=180 \degree\\ \sf 2x=90\degree \\ \boxed{ \red{\sf x= 45\degree}}$

$\sf So, ∠1 = ∠2 = 45 \degree\\ \sf∠1 = ∠DAC =∠DCA = 45 \degree$

Therefore, angle DAC = 45°

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Hope it elps! ;)