Question

The two angle of an obtuse angled triangle , whose obtuse angle measure 131°,are in the ratio 2:5. Find the angles.​

Answer 1

${\red{\underline{\underline{\bold{Given:-}}}}}$

• The obtuse angle of a triangle = 131°

• The two acute angles of a triangle are in the ratio 2:5

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The acute angles of the triangle

${\green{\underline{\underline{\bold{Solution:-}}}}}$

Let the acute angles be 2x and 5x

As we know that the sum of angles in a triangle = 180°

➪ $\bf 131 \degree + 2x + 5x = 180 \degree$

➪ $\bf131\degree + 7x = 180 \degree$

➪ $\bf7x = 180 \degree - 131 \degree$

➪ $\bf7x = 49 \degree$

➪ $\bf x = \frac{49}{7} = 7 \degree$

The two acute angles are:-

➪ 2x = 2×7 = 14°

➪ 5x = 5×7 = 35°

Therefore:-

$\bf The \:acute\: angles \:are\: 14\degree\: and \:35\degree$

Answer 2

${\red{\underline{\underline{\bold{Given:-}}}}}$

• The obtuse angle of a triangle = 131°

• The two acute angles of a triangle are in the ratio 2:5

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The acute angles of the triangle

${\green{\underline{\underline{\bold{Solution:-}}}}}$

Let the acute angles be 2x and 5x

As we know that the sum of angles in a triangle = 180°

➪ 131 degree + 2x + 5x = 180 degree131°+2x+5x=180°

➪ degree + 7x = 180 degree131°+7x=180°

➪ x = 180 degree - 131 degree7x=180°−131°

➪ 7x = 49 degree7x=49°

➪ x= 49/= 7 \degreex= 7

49

=7°

The two acute angles are:-

➪ 2x = 2×7 = 14°

➪ 5x = 5×7 = 35°

Therefore:-

The acute angles are 14 degree and 35degree Theacute angles are 14°and35°