Question

In △ABC , line AB is extended up to point E and line BC is extended up to D . The measure of some of the angles is given as; ∠BAC=70° and ∠EBC=120° .
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Answer 1

Answer:

$\angle ACD = 130 ^\circ$.

Step-by-step explanation:

$\angle ABC$ and $\angle EBC$ are supplementary angles. Their sum should be $180^\circ$.  $\angle EBC = 120^\circ$ $\implies \angle ABC = 180^\circ - \angle EBC = 180^\circ - 120^\circ = 60^\circ$.

The sum of the three angles in triangle $\triangle ABC$: $(\angle ABC + \angle BAC + \angle ACB)$ should be equal to $180^\circ$.

$\angle ABC = 60^\circ$ and $\angle BAC = 70^\circ$ $\implies \angle ACB = 180^\circ - \angle ABC - \angle ACB = 180^\circ - 70^\circ - 60^\circ = 50^\circ$.

$\angle ACB$ and $\angle ACD$ form another pair of supplementary angles. Their sum should also be $180^\circ$. $\angle ACB = 50^\circ$ $\implies \angle ACD = 180^\circ - \angle ACB = 180^\circ - 50^\circ = 130^\circ$.