Question

the measures of interior angles of a triangle are in the ratio 3: 4: 5 find the measure of its largest angle

Answer 1

3x+4x+5x=180 (A.S.A.)
12x=180
x=180/12
x=15
Since the ratio are as 3:4:5 and five is largest therefore the largest angle will be in ratio 5
15*5=75°

Answer 2

Concept :

Two rays that have a common endpoint and are referenced to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the region where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. An interior angle is one that is located inside a polygon. As an illustration, a triangle has three interior angles. The alternative definition of sides and angles is "angles contained in the interior area of both parallel lines when a transversal is intersected are known as internal angles." In geometry, a polygon's angle is made up of two of its sides that have a common terminal. If a position inside the angle is inside the polygon's interior, the angle is referred to as an interior angle for a simple polygon, whether it is regular or not.

Given:

the measures of interior angles of a triangle are in the ratio $3: 4: 5$.

Find, the measure of its largest angle.

Solution:

According to the problem,

the measures of interior angles of a triangle are in the ratio $3: 4: 5$

We all know that the sum of the interior angles of a triangle is $180$°.

By applying the formula,

$3x+4x+5x=180$

$12x=180\\x=180/12\\x=15$

Since the ratio are as $3:4:5$ and five is the largest therefore the largest angle will be in the ratio $5$

So, the measure of its largest angle = ( $15$ × $5 ) = 75$ °

Hence the measure of its largest angle is $75$ °

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