(a) Can a triangle have two obtuse angles? Justify your answer.
(b) In a $△ A B C$ the side BC is extended to D. Given that $∠ A B C = 30^{\circ} a n d ∠ A C D = 160^{\circ}$ . Find $∠ B A C$ . [3 MARKS]

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Solution

(a) Answer: 1 Mark
Reason: 1 Mark
(b) Solution: 1 Mark

(a) A triangle can have only one obtuse angle.

If we have more than one obtuse angle in a triangle, then the sum of two (obtuse) angles will exceed $180^{\circ}$ .

Since the sum of all angles of a triangle is $180^{\circ}$ .

$\Rightarrow$ A triangle cannot have more than one obtuse angle.

(b)

$∠ B C D = 180^{\circ}$ (Straight angle)
$∴ ∠ A C B = ∠ B C D - ∠ A C D = (180 - 160)^{\circ} = 20^{\circ}$
$\Rightarrow ∠ B A C = 180^{\circ} - (∠ A B C + ∠ A C B) = 180 - (30 + 20) = 180 - 50 = 130$
$∴ ∠ B A C = 130^{\circ}$

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(a) Can a triangle have two obtuse angles? Justify your answer. (b) In a △ABC the side BC is extended to D. Given that ∠ABC=30∘ and ∠ACD=160∘. Find ∠BAC. [3 MARKS]

(a) Can a triangle have two obtuse angles? Justify your answer.
(b) In a $△ A B C$ the side BC is extended to D. Given that $∠ A B C = 30^{\circ} a n d ∠ A C D = 160^{\circ}$ . Find $∠ B A C$ . [3 MARKS]