Question

one of the exterior angles of a traingle is 125° and the interior opposite angles are in the ratio 2:3. find the angles of the traingle​

Answer 1

hi here is your answer!

Answer:

The interior opposite angles are 50⁰ and 75⁰ respectively

Step-by-step explanation:

Let the interior opposite angles be 2x and 3x

we know that, exterior angles = sum of opposite interior angles

2x+3x=125

5x=125

x=125/5

x=25

substituting x value in 2x and 3x

2x= 2(25) =50

3x=3(25) = 75

you can even check by adding 50+75=125

i hope it helps.

Answer 2

Given: one of the exterior angles of a traingle is 125° and the interior opposite angles are in the ratio 2:3.

To Find: the angles of the traingle respectively

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❒ Let the opposite interior angles in the triangle be 2x and 3x respectively

${ \underline{ \bf{ \bigstar \: According \: to \: the \: question : }}}$

• The measure of an exterior angle is 125°

Now, Basing this let's find the measure of the interior ∠ACB

We know that,

• The sum of the measurements of a interior angle and it's adjacent exterior angle equals 180°

$\leadsto \tt 125 \degree \: + \angle \: c = 180\degree \\ \\ \leadsto \tt \angle \: c = 180 - 125 \degree \: \: \: \\ \\ \leadsto \tt \angle \: c = { \blue{ \boxed{55\degree}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Now, let's find the measurements of the other interior angles.

${ \underline{ \frak{As \: we \: know \: that \dag}}}$

• The sum of the measurements of all the interior angles in a triangle equal 180°

${ \underline{ \bf{ \bigstar \:Framing \: an \: equation \: we \: get : }}}$

${ : \implies} \sf \: 55 + 2x + 3x = 180 \\ \\ \\ { : \implies} \sf \: 55 + 5x = 180 \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: 5x = 180 - 55 \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: 5x = 125 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: \: x = \cancel\frac{125}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: { \underline{ \pink{ \boxed{ \frak{x = 25}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now,

• Let's substitute the value of x and find the measurements of the angles.

${\purple{\mapsto}} \tt \: angle \: 2x = 2(25) = 50 \degree \\ \\ {\purple{\mapsto}} \tt \: angle \: 3x = 3(25) = 75 \degree$

${ \underline{ \bf{ \bigstar \: Verification : }}}$

• Now let's add all the angles and check weather they equal 180° or not.

$\leadsto \tt 55 + 75 + 50 = 180 \\ \\ \\ \leadsto \tt 130 + 50 = 180 \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt 180 = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence verified..!!

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