Question

The largest and the smallest angles of a triangle are in the ratio of 3:1 respectively. The second largest angle of
the triangle is equal to 44
.What is the value of 150 per cent of the largest angle of the triangle?
(1) 149 (2) 129 (3) 153 (4) 173 (5) None of these

Answer 1

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Answer 2

Concept:

Angle sum property of a triangle: This property states that the sum of all the interior angles of a triangle (acute, obtuse, or a right triangle) is always 180°.

This property is one of the commonly utilized properties in geometry. The most common application of the angle sum property is to calculate unknown angles.

Given:

The ratio of largest and smallest angle = 3:1

The second-largest angle = 44°

To find:

The value of 150% of the largest angle of the triangle.

Solution:

Let the smallest angle be x.

Largest angle = 3x

( ∵ The ratio of largest and smallest angle = 3:1 )

Applying the angle sum property

$x+3x+44=180\\4x=180-44\\4x=136\\x=\frac{136}{4} \\x=34$

∴ Smallest angle = 34°

As the largest angle = 3x

Largest angle = $3$ × $34=102$°

Calculate 150% of the largest angle

$\frac{150}{100}$ × $102$

= $\frac{15300}{100}$

= $153$

Hence the value of 150% of the largest angle of the triangle is 153.