Question

# (a) Find x in the below diagram. What are such triangles called? (b) In a triangle ABC, an altitude is dropped from A to BC at D. ∠A=40∘,∠B=(2x+4)∘,∠C=(4x−k)∘,∠BAD=30∘ Find k , x and the values of the angles. [4 MARKS]

Solution

## (a) Solution: 1 Mark      Type of triangle: 1 Mark (b) Solution: 1 Mark      Correct answer: 1 Mark (a) For a triangle, sum of all angles = 180o Or, (2x - 15o) + (x + 20o) + (x + 15o) = 180o Or, 2x + x + x - 15o + 20o + 15o = 180o Or, 4x + 20o = 180o Or, 4x = 160o Or, x = 1604 = 40o The angles of the triangle will be, (2x - 15o = 65o), (x + 20o = 60o) and (x + 15o = 55o) Since all angles are less than 90o, it's an 'acute angled triangle' and also all the angles are of different values therefore all the sides will be of different length, hence it is a 'scalene triangle'. (b               In triangle ABD ⇒2x+4+90+30=180 ⇒2x=180−124 ⇒x=562 ⇒x=28 In triangle ADC ⇒4x−k+90+10=180 ⇒4x−k=180−100 ⇒4(28)−k=80 (Substituting the value of x=28) ⇒k=4(28)−80 ⇒k=112−80 ⇒k=32 ∴ The angles are 40∘,60∘ and 80∘ for the given triangle.Mathematics

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