Question

the angle of a triangle are in the ratio 3:4:5 find the measure of an angle a,b,c
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Answer 1

Answer:

Let angle be x

3x+4x+5x=180

12x=180

180/12=x

          =15

3x=15 x 3=45

4x=4 x 15=60

5x=5 x 15=75

Step-by-step explanation:

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Answer 2

Given: The angles of a triangle are in the ratio 3:4:5.

Need to find: The measures of the angles.

❒ Let the angles of a triangle are 3x, 4x and 5x.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

⠀

• Sum of all angles of the triangle is 180°.

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Therefore,

⠀

$:\implies\sf 3x + 4x + 5x = 180^{\circ} \\\\\\:\implies\sf 12x = 180^{\circ} \\\\\\:\implies\sf x = \cancel\dfrac{180^{\circ}}{12} \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 15^{\circ}}}}}}\;\bigstar$

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$\bigstar\: \underline{\textbf{Angles of triangle are \; :}}$

• First angle, 3x = 3(15) = 45°

• Second angle, 4x = 4(15) = 60°

• Third angle, 5x = 5(15) = 75°

⠀

$\therefore{\underline{\sf{Hence,\; angles\; of \; the \; \triangle\; are\; \bf{45^{\circ}, \: 60^{\circ}\; and\; 75^{\circ} }.}}}$