A man runs in the east direction and suddenly changes his direction towards the north. After running for some time, he comes back to his original position. Given that the man's path of running is a triangle and one of its angles is 90 degrees, find the sum of the other two angles. [3 MARKS]

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Solution

Properties: 1 Mark
Sum: 2 Marks

The given conditions make a right-angled triangle because one of its angles is $90^{\circ}$

Using the angle sum property of a triangle,
$∠ O + ∠ A + ∠ B = 180^{\circ}$

$∠ O + 90^{\circ} + ∠ B = 180^{\circ}$

$∠ O + ∠ B = 90^{\circ}$

Sum of the other two angles will be $90^{\circ}$

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A man runs in the east direction and suddenly changes his direction towards the north. After running for some time, he comes back to his original position. Given that the man's path of running is a triangle and one of its angles is 90 degrees, find the sum of the other two angles. [3 MARKS]

Properties: 1 Mark Sum: 2 Marks The given conditions make a right-angled triangle because one of its angles is90∘ Using the angle sum property of a triangle, ∠O+∠A+∠B=180∘ ∠O+90∘+∠B=180∘ ∠O+∠B=90∘ Sum of the other two angles will be 90∘