Mathematics

State True or False
From the following figure, we can say:  $$ \angle ACD= \angle CBE  $$


ANSWER

True


SOLUTION
In $$\triangle$$ ABC,
AB = AC
thus, $$\angle ABC = \angle ACB = x $$ (Opposite angles of equal sides are equal)
Now, $$\angle ABC + \angle CBE = 180 $$ (Angles on a straight line)
$$x + \angle CBE = 180 $$
$$\angle CBE = 180 - x$$ (I)
Also, $$\angle ACB + \angle ACD = 180 $$ (Angles on a straight line)
$$x + \angle ACD = 180 $$
$$\angle ACD = 180 - x$$ (II)
Hence, from I and II
$$\angle ACD = \angle CBE $$
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TRUE/FALSE Medium Published on 09th 09, 2020
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