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

sum should also be . .

Explanation:

Answer 2

`\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`.