Question

11. In a triangle, one the angle is
60°. The other two angles are in
the ratio 7:5. Find the two
angles.​

Answer 1

Step-by-step explanation:

given <1=60

other two angle are 7x,5x

In triangle sum of all angles=180

60+7x+5x=180

12x=180-60

12x=120

x=120/12

x=10

7x=7×10=70

5x=5×10=50

Answer 2

$\sf \pink{Given}\begin{cases}&\sf{One\ angle\ of\ the\ triangle=\bf{60\degree.}} \\ \\ &\sf{Ratio\:of\:other\:two\:angles=\bf{7:5.}}\end{cases}$

To FinD:-

The two angles.

SolutioN:-

• Let the other two angles be 7x, 5x.

We know that,

• All angles in a triangle sum upto 180°.

☯ According to the question,

$\\ :\normalsize\implies{\sf{7x+5x+60\degree=180\degree}}$

$\\ :\normalsize\implies{\sf{12x=180\degree-60\degree}}$

$\\ \quad:\normalsize\implies{\sf{12x=120\degree}}$

$\\ \quad \ \ :\normalsize\implies{\sf{x=\dfrac{120}{12}}}$

$\\ \qquad \ \ :\normalsize\implies{\sf{x=\cancel{\dfrac{120}{12}}}}$

$\\ \qquad\quad\quad\normalsize\therefore\boxed{\mathfrak{\pink{x=10.}}}$

The angles are :

1. 7x = 7 × 10 = 70°
2. 5x = 5 × 10 = 50°

VerificatioN:-

$\\ :\normalsize\implies{\sf{70\degree+50\degree+60\degree=180\degree}}$

$\\ \qquad:\normalsize\implies{\sf{180\degree=180\degree}}$

$\\ \qquad\quad\quad\normalsize\therefore\boxed{\mathfrak{\pink{LHS=RHS.}}}$

• Hence verified.

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The two angles are 70° and 50°.