Question

One angle of a triange is 9 degrees, a second angle is 99 degrees. What is the measurement of the third angle?

Answer 1

Step-by-step explanation

Step 1

The sum of all the internal angles of a simple polygon is 180(n–2)°, where n is the number of sides.

so, for a triangle, the number of sides (n) is 3, then

replacing

`\begin{gathered} \text{ Sum of internal angles=180(3-1)=180}\cdot2=360 \\ so,\text{ Sum of internal angles=}180 \end{gathered}`

Step 2

Also, we have

`\begin{gathered} \text{angle}=\text{ 9 \degree} \\ \text{angle}2=99\text{ \degree} \\ \text{angle}3=\text{ x} \\ \text{hence,} \\ \text{angle1+angle2+angle3=180} \\ \text{replace} \\ 9+99+x=180 \\ 108+x=180 \end{gathered}`

finally,solve for x

`\begin{gathered} 108+x=180 \\ \text{subtract 108 in both sides} \\ 108+x-108=180-108 \\ x=72 \end{gathered}`

therefore, the measurement of the third angle is 72 °

I hope this helps you

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