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Komok [63]
3 years ago
9

Looking at the angle relationship below, what is the value of x? Q 107 x

Mathematics
1 answer:
Vlad1618 [11]3 years ago
7 0

Answer:

73 degrees.

Step-by-step explanation:

If they're on a line together, they add up to 180 degrees. You can do 180 - 107 = 73 degrees.

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In a ∆ABC , angle A + Angle B = 125° and Angle B + Angle C = 150° . Find all the angles of ∆ABC.​
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\large\underline{\sf{Solution-}}

Given that,

<em>In triangle ABC</em>

\purple{\rm :\longmapsto\:\angle A + \angle B = 125 \degree \: -  -  - (1) }

\purple{\rm :\longmapsto\:\angle B + \angle C = 150 \degree \:  -  -  - (2)}

We know,

Sum of all interior angles of a triangle is supplementary.

\purple{\rm :\longmapsto\:\angle A + \angle B + \angle C = 180\degree }

<u>On adding equation (1) and (2), we get </u>

\purple{\rm :\longmapsto\:\angle A + \angle B + \angle B + \angle C = 125\degree  + 150 \degree \:}

\purple{\rm :\longmapsto\:\angle A + \angle B + \angle C + \angle B = 275\degree \:}

\purple{\rm :\longmapsto\:180\degree + \angle B = 275\degree \:}

\purple{\rm :\longmapsto\:\angle B = 275\degree - 180\degree  \:}

\purple{\rm :\longmapsto\:\angle B = 95\degree  \:}

On substituting the value in equation (1) and (2), we get

\purple{\rm :\longmapsto\:\angle A + 95\degree  = 125\degree }

\purple{\rm :\longmapsto\:\angle A =  125\degree - 95\degree  }

\purple{\rm :\longmapsto\:\angle A =  30\degree  }

Also, from equation (2), we get

\purple{\rm :\longmapsto\:95\degree  + \angle C = 150\degree }

\purple{\rm :\longmapsto\:\angle C = 150\degree  - 95\degree }

\purple{\rm :\longmapsto\:\angle C = 55\degree }

Hence,

\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{\angle A = 30\degree }  \\ \\ &\sf{\angle B = 95\degree } \\ \\ &\sf{\angle C = 55\degree } \end{cases}\end{gathered}\end{gathered}

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Step-by-step explanation:

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