Question

One angle of triangle is 54 degree of the other two angles are in the ratio 5ratio 2 find other two
angles of triangle

Answer 1

Required Answer:

$\boxed { \rm \blue { Given:}}$

• One angle of a ∆ is 54°.

• Other two angles are in the ratio of 5:2.

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$\boxed { \rm \pink { To \: find :}}$

• Measure of the other two angles

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$\boxed { \rm \orange { Calculation:}}$

→ Let the other two angles be 5x° and 2x°.

As we know that,

$\large {\bigstar}$ $\boxed { \sf { Sum \: of \: interior \: angles \: of \: \triangle = 180°}}$

Substituting values:

$\sf { \longrightarrow 54° + 5x° + 2x° = 180°}$

$\sf { \longrightarrow 54° + 7x° = 180°}$

$\sf { \longrightarrow 7x° = 180° - 54°}$

$\sf { \longrightarrow 7x° = 126°}$

$\sf { \longrightarrow x° = \dfrac{126°}{7} }$

$\sf \red { \longrightarrow x° = 18° }$

Therefore, the value of x° is 18°. So, the other two angles of the triangle are:–

• Second angle = 5x°

→ Second angle = 5 × 18

→ Second angle = 90°

• Third angle = 2x°

→ Third angle = 2 × 18

→ Third angle = 36°

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$\boxed { \rm \purple { Quick \: Check!}}$

We know:

$\large {\bigstar}$ $\boxed { \sf { Sum \: of \: interior \: angles \: of \: \triangle = 180°}}$

$\sf {\longrightarrow 36° + 90° + 54° = 180°}$

$\sf {\longrightarrow 90° + 90° = 180°}$

$\sf \red {\longrightarrow 180° = 180°}$

$\sf { \: \: \: \: \: \: \: \: \: \: \: Hence, verified!}$

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$\boxed { \rm \green { More \: about \: triangles!}}$

• Perimeter of triangle = Sum of all sides

• Area of triangle = $\sf { \dfrac{1}{2} \times b \times h}$

Some important properties to remember:

★ Angle sum property of ∆ :

• Sum of interior angles of ∆ = 180°

★ Exterior angle property of ∆ :

• Sum of two interior opposite angles = Exterior angle

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Answer 2

We have,

• One of the angles = 54°
• Ratio of other two = 5:2

Let, common be = k

∴ Angles = 5k, 2k.

We know, sum of interior angles of a △ = 180°

∴ 5k + 2k + 54° = 180°

⇒ 7k = 180° - 54°

⇒ 7k = 126°

⇒ k = 126°/7 = 18°

So, the angles are:-

• 5k = 5 × 18° = 90°
• 2k = 2 × 18° = 36°