Question

The two acute angles of an obtuse angled triangle,whose obtuse angle measures 131 degree are in the ratio 2:5 find the angles​

Answer 1

Answer:

$\orange{ \sf \: 1nd \: accute \: \: angle \: is \: 2x \: = 2 \times 7 = 14}$

$\orange{ \sf \: 2nd \: accute \: \: angle \: is \: 5x \: = 5 \times 7 = 35}$

Step-by-step explanation:

$\sf \: Let \: the \: angles \: be \: 2x \: and \: 5x$

$\green{\boxed {\underline{ \sf \: sum \: of \: angles \: of \: triangle \: is \: 108 \: degree}}}$

$\large{ \sf \: So,}$

$\implies \: \sf131 {}^{0} + 2x + 5x = 180$

$\sf\implies7x = 180 - 131$

$\sf \: \implies7x \: = \: 49$

$\sf \: x \: = \: \cancel\frac{49}{7}^{7}$

$\boxed{ \large\sf \: x \: = \: 7}$

$\green{\sf \: 1st \: accute \: angle \: is \: 2x \: = 2 \times 7 = 14}$

$\green{ \sf \: 2nd \: accute \: \: angle \: is \: 5x \: = 5 \times 7 = 35}$