Question

⭐in a triangle the measure of the greatest angle is square of the measure of the smallest angle, and the other angle is double of the smallest angle. Find the greatest angle. ⭐

CLASS 10 CHAPTER :QUADRATIC EQUATIONS

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Answer 1

According to the question,

1 ) -The measure of the greatest angle is square of the measure of the smallest angle.

2 ) -  the other angle is double of the smallest angle.

Let,

   Measure of smallest angle = x°

   Measure of largest angle = ( x^2 )°

   Measure of other( 3rd ) angle = 2x°

From the properties of triangles, we know that the sum of all angles( at vertices ) of a triangle is 180°.

∴ 1st angle + 2nd angle + 3rd angle = 180°

⇒ x^2 + x + 2x  = 180

⇒ x^2 + 3x - 180 = 0

⇒ x^2 + ( 15 - 12 )x - 180 = 0

⇒ x^2 + 15x - 12x - 180 = 0

⇒ x( x + 15 ) - 12( x + 15 ) = 0

⇒ ( x - 12 )( x + 15 ) = 0

∴ x = 12 Or x = - 15

Angles can't be measured negatively, therefore x = 12.

Measure of smallest angle = x° = 12°

Measure of 3rd angle = 2x° = 2( 12 )° = 24°

Measure of greatest angle = x^2 = 12^2 = 144°

Answer : The greatest angle is 144°

$\:$

Answer 2

$\huge{\mathfrak{Heya!!}}$
.

$let \: the \: measure \: of \: the \: smallest \: angle \: be \: x \\ \\ according \: to \: question \\ \\ the \: largest \: angle \: = \: {x}^{2} \\ the \: other \: angle \: = 2x \\ \\ \\ as \: we \: know \: tha t \\ \: sum \: of \: all \: the \: angles \: of \: a \: triangle \: = 180 \: deg. \\ \\ so \\ x + {x}^{2} + 2x = 180 \\ \\ {x}^{2} + 3x - 180 = 0 \\ \\ {x}^{2} + (15 - 12)x - 180 = 0 \\ \\ {x}^{2} + 15x - 12x - 180 = 0 \\ \\ x(x + 15) - 12(x + 15) = 0 \\ \\ (x + 15)(x - 12) = 0 \\ \\ \\ so \: x = 12 \\ \\ not \: - 15 \: because \: angle \: cannot \: be \: negative \\ \\ \\ \\ so \: smaller angle \: is \: 12°$

as we got the measure of smaller angle I.e 12 °

We can find other angles

so,

the measure of larger angle =x^2=(12)^2=144°

$\bf{the\: measure \:of\: other\: angle\:=2x=2*12=24°}$

Hope it helps u. :-)

THANKS. :-)