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 About the author Rose
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. Reply
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 ⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀ ❒ Let the opposite interior angles in the triangle be 2x and 3x respectively [tex]{ \underline{ \bf{ \bigstar \: According \: to \: the \: question : }}}[/tex] 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° [tex] \leadsto \tt 125 \degree \: + \angle \: c = 180\degree \\ \\ \leadsto \tt \angle \: c = 180 – 125 \degree \: \: \: \\ \\ \leadsto \tt \angle \: c = { \blue{ \boxed{55\degree}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex] Now, let’s find the measurements of the other interior angles. [tex] \\ [/tex] [tex]{ \underline{ \frak{As \: we \: know \: that \dag}}} [/tex] The sum of the measurements of all the interior angles in a triangle equal 180° [tex]{ \underline{ \bf{ \bigstar \:Framing \: an \: equation \: we \: get : }}}[/tex] [tex]{ : \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}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex] [tex] \\ [/tex] Now, Let’s substitute the value of x and find the measurements of the angles. [tex] {\purple{\mapsto}} \tt \: angle \: 2x = 2(25) = 50 \degree \\ \\ {\purple{\mapsto}} \tt \: angle \: 3x = 3(25) = 75 \degree[/tex] [tex] \\ [/tex] [tex]{ \underline{ \bf{ \bigstar \: Verification : }}}[/tex] Now let’s add all the angles and check weather they equal 180° or not. [tex]\leadsto \tt 55 + 75 + 50 = 180 \\ \\ \\ \leadsto \tt 130 + 50 = 180 \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt 180 = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex] Hence verified..!! ⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀ Reply
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.
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
⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀
❒ Let the opposite interior angles in the triangle be 2x and 3x respectively
[tex]{ \underline{ \bf{ \bigstar \: According \: to \: the \: question : }}}[/tex]
Now, Basing this let’s find the measure of the interior ∠ACB
We know that,
[tex] \leadsto \tt 125 \degree \: + \angle \: c = 180\degree \\ \\ \leadsto \tt \angle \: c = 180 – 125 \degree \: \: \: \\ \\ \leadsto \tt \angle \: c = { \blue{ \boxed{55\degree}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \\ [/tex]
[tex]{ \underline{ \frak{As \: we \: know \: that \dag}}} [/tex]
[tex]{ \underline{ \bf{ \bigstar \:Framing \: an \: equation \: we \: get : }}}[/tex]
[tex]{ : \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}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \\ [/tex]
Now,
[tex] {\purple{\mapsto}} \tt \: angle \: 2x = 2(25) = 50 \degree \\ \\ {\purple{\mapsto}} \tt \: angle \: 3x = 3(25) = 75 \degree[/tex]
[tex] \\ [/tex]
[tex]{ \underline{ \bf{ \bigstar \: Verification : }}}[/tex]
[tex]\leadsto \tt 55 + 75 + 50 = 180 \\ \\ \\ \leadsto \tt 130 + 50 = 180 \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt 180 = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
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