Question

11. If one angle of a triangle is 60° and the other two angles are in the ratio 2:3, find
these angles.
Find the measure of each of the equal angles.​

Answer 1

Given:

One of the angles of a triangle = 60°

Ratio of other two angles = 2:3

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To find:

The other two angles.

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Solution:

Let the other two angles be 2x and 3x.

As we know that, sum of all the angles in a triangle is 180°, so,

60°+2x+3x = 180°

60°+5x = 180°

5x = 180°-60°

5x = 120°

$x = \dfrac{120}{5}$

$\boxed {\boxed {\sf {\orange {x=24°}}}}$

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Verification:

On substituting the value of x as 24 in the equation,

60°+2x+3x = 180°

60°+2×24°+3×24° = 180°

60°+48°+72° = 180°

180° = 180°

LHS = RHS

Hence Verified!

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Final answer:

• First angle = 60°
• Second angle = 2×24°

= 48°

• Third angle = 3×24°

= 72°

$\sf \green {Therefore\ the\ angles\ of\ the\ triangle\ are\ 60°, 48°\ and\ 72°.}$

Answer 2

Given:

• One angle of a triangle = 60°
• Other two angles are in the ratio = 2:3

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To find:

• The the measures of other two angles.

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Solution:

Let the measures of other two angles be 2x and 3x.

$\bold{\underline{The\:sum\:of\:three\:angles\:of\:a\: triangle\:is\:180°}}$

So,

$\sf\implies 60° + 2x + 3x = 180°$

$\sf\implies 60° + 5x = 180°$

$\sf\implies 5x = 180° - 60°$

$\sf\implies 5x = 120°$

$\sf\implies x = \frac{120}{5}$

$\large\underline{\boxed{\sf{\red{x=24}}}}$

Now we got the value of 'x'. So, now let's find the measure of,

• Second angle (2x):

$\sf\rightarrow 2x$

$\sf\rightarrow 2×24$

$\sf\rightarrow 48°$

• Third angle (3x):

$\sf\rightarrow 3x$

$\sf\rightarrow 3×24$

$\sf\rightarrow 72°$

Therefore, the measures of three angles of a triangle are $\bold{\green{60°}}$, $\bold{\green{24°}}$ and $\bold{\green{72°}}$.

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Verification:

$\sf\implies Sum\:of\:three\:angles = 180°$

$\sf\implies 60° + 48° + 72° = 180°$

$\sf\implies 180° = 180°$

$\bold{\implies L.H.S = R.H.S}$

• $\large{\underline{\underline{\tt{\red{Hence,\: verified\:!}}}}}$

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