Question

And the iceul
9. If one angle of a triangle is 60° and the other two angles are in the ratio 2:3. find
these angles.
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Answer 1

Answer:

48° , 72°

Step-by-step explanation:

All the angles of triangle are 180°

Here, given, Let ∠A = 60°, ∠B = 2x, ∠C=3x

As ratio of Angles B and C are 2:3

So,

60 + 2x +3x = 180

5x = 120

x = 24°

Hence, ∠B = 2 × 24° = 48°

∠C = 3 × 24° = 72°

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Answer 2

Appropriate Question:

• If one angle of a triangle is 60° and the other two angles are in the ratio of 2: 3. Find these angles.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀

Given: One angle of a triangle is 60° and the other two angles are in the ratio of 2: 3.

Need to find: All angles of triangle.

❍ Let's say, that two angles of the traingle be 2x and 3x respectively.

⠀

A N G L E⠀S U M⠀P R O P E R T Y :

• Angle sum property of a triangle says that the sum of all three angle of a triangle is equal to 180°.

⠀⠀⠀

$\dashrightarrow\sf 2x + 3x + 60^\circ = 180^\circ \\\\\\\dashrightarrow\sf 5x + 60^\circ = 180^\circ \\\\\\\dashrightarrow\sf 5x = 180^\circ - 60^\circ \\\\\\\dashrightarrow\sf 5x = 120^\circ \\\\\\\dashrightarrow\sf x = \cancel\dfrac{120}{5} \\\\\\\dashrightarrow\underline{\boxed{\frak{\purple{x = 24}}}}\;\bigstar$

⠀⠀⠀

Therefore,

• First angle, 2x = 2(24) = 48°
• Second angle, 3x = 3(25) = 72°
• Third angle is given = 60°

⠀⠀⠀

∴ Hence, the three angles of the given triangle are 48°, 72° and 60° respectively.

⠀

$\rule{250px}{.3ex}$

⠀⠀⠀

★ V E R I F I C A T I O N :

⠀

$:\implies\sf \Big\{First\;angle\Big\} +\Big\{Second\;angle\Big\} +\Big\{Third\;angle\Big\} = \Big\{Sum\Big \}\\\\\\:\implies\sf 48^\circ + 72^\circ + 60^\circ = 180^\circ \\\\\\:\implies\sf 108^\circ + 72^\circ = 180^\circ\\\\\\:\implies\underline{\boxed{\pmb{\sf{180^\circ = 180^\circ}}}}$

⠀

⠀⠀⠀⠀$\;\quad\qquad\qquad\qquad\quad\pmb{\sf{Hence\; Verified!}}$