Question

if one of the angle of a triangle of a triangle is 45 digri and
other two angle are in the ratio 4:5 find the measure of all the angle​

Answer 1

Answer:

let the common ratio is x

so other two angles are 4x° and 5x°

sum of the three angles of a triangle is 180°

here,

45+4x+5x=180

=> 9x=180-45

=> 9x=135

=> x=135/9

=> x=15

so the angles are 45°, 4×15°=60° and 5×15°=75°

Answer 2

Given: The one angle of the triangle is 45° and other two angles of the triangle are in the ratio of 4 : 5.

☢ Let the another two angles of the triangle be 4n and 5n.

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$\bigstar\;{\underline{\underline{\cal{\:\;ANGLE \: SUM \: PROPERTY \::}}}}$

$:\implies\sf\quad \angle A + \angle B + \angle C = 180^\circ$

$:\implies\sf\quad 4n + 5n + 45^\circ = 180^\circ$

$:\implies\sf\quad 9n + 45^\circ = 180^\circ$

$:\implies\sf\quad 9n = 180^\circ - 45^\circ$

$:\implies\sf\quad 9n = 135^\circ$

$:\implies\sf\quad n = \cancel\dfrac{135^\circ}{9}$

$:\implies\quad\underline{\boxed{\pmb{\sf{n = 15^\circ}}}}$

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$\underline{\bigstar\:\frak{~Angles\;of\;the\:\triangle\; :}}$

$\qquad\bullet\:\;\sf 4n = 4\times 15 = 60^\circ$

$\qquad\bullet\;\:\sf 5n = 5 \times 15 = 75^\circ$

$\therefore\:\underline{\sf{Hence, \: the \: other \: two \: angles \: are \: {\pmb{\sf{60^\circ}} and\:{\pmb{\sf{75^\circ}} respectively}}}}.$