Question

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7. One of the exterior angles of a triangle is 80° and the interior opposite angles
in the ratio 5:3. Find the angles of the triangle.
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Answer 1

Appropriate Question:

• One of the exterior angles of a triangle is 80° and the interior opposite angles in the ratio 5:3. Find the angles of the triangle.

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Given: Exterior angle of the triangle is 80°. And, interior angles are in the ratio of 5:3.

To find: The angles of the triangle.

Let the interior opposite angles be 5x and 3x respectively.

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

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• Sum of all interior opposite angles is equal to the exterior angle.
• And, Exterior angle is given which is 80°.

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Therefore,

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$:\implies\sf 5x + 3x = 80 \\\\\\:\implies\sf 8x = 80 \\\\\\:\implies\sf x = \cancel\dfrac{80}{8} \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 10}}}}}\;\bigstar$

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$\underline{\bf{\dag} \:\mathfrak{Interior\; Angles\; of \; the \; \triangle \; are\: :}}$⠀⠀

• First angle, 5x = 5(10) = 50°

• Second angle, 3x = 3(10) = 30°

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Let the third angle of the triangle be C.

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

Therefore,

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$:\implies\sf 50 + 30 + \angle C = 180\\\\\\:\implies\sf 80 + \angle C = 180 \\\\\\:\implies\sf \angle C = 180 - 80\\\\\\:\implies{\underline{\boxed{\frak{\pink{ \angle C = 100^{\circ}}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence, \; angles \; of \; \triangle\; are\; \bf{100^{\circ}, 30^{\circ}\;\&\;50^{\circ} }.}}}$

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Answer 2

..QUESTION..

One of the exterior angles of a triangle is 80⁰ and the interior opposite angles are in the ratio of 5 : 3 . Find the angles of the triangle.

..ANSWER..

Given , here

ㅤㅤㅤ➪ Exterior angle = 80⁰

☯︎ Ratio of the interior opposite angles = 5:3

♧︎︎︎ Let the angles be " x "

߷ㅤㅤㅤ First angle = 5x

ㅤㅤㅤㅤ Second angle = 3x

★ We know that ,

➪ Exterior angle = sum of interior opposite angles

•°• According to the Question ,

ㅤㅤㅤ➪ 80⁰ = 5x + 3x

ㅤㅤㅤ➪ 5x + 3x = 80⁰

ㅤㅤㅤ➪ 8xㅤㅤ = 80⁰

ㅤㅤㅤ➪ xㅤㅤ = 80 / 8

ㅤㅤㅤ➪ x ㅤㅤ= 10

• we got ➪ x = 10

•°• First angle = 5x

ㅤㅤㅤㅤㅤㅤㅤ= 5 × 10

ㅤㅤㅤㅤㅤㅤㅤ= 50⁰

AND ,

➪ Second angle = 3x

ㅤㅤㅤㅤㅤㅤㅤㅤ = 3 × 10

ㅤㅤㅤㅤㅤㅤㅤㅤ = 30⁰

Also , Let the third angle be " y "

•°• value of the third angle »

➪ 1st angle + 2nd angle + 3rd angle = 180⁰

[ angle sum property of a triangle ]

ㅤㅤㅤ➪ 50⁰ + 30⁰ + y = 180⁰

ㅤㅤㅤ➪ 80⁰ + y = 180⁰

ㅤㅤㅤ➪ y = 180⁰ - 80⁰

ㅤㅤㅤ➪ y = 100⁰

•°• First angle = 50⁰

➪ Second angle = 30⁰

➪ Third angle = 100⁰

ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂