Question

Did you get the same sum for both sets of angle measurements? What do you think that means? Create an equation to represent the situation.

Answer 1

The equation representing the sum of the angles in triangle TVW is
`\(T + V + W = 180^\circ\)`, which holds true for valid angle measurements within the triangle.

Yes, for both sets of angle measurements, the sum of the angles T, V, and W equals
`\(180^\circ\).` This consistency indicates that both sets of measurements represent valid angles within a triangle.

To create an equation representing this situation, you can use the fact that the sum of the interior angles of a triangle is always
`\(180^\circ\).`

The equation representing the sum of the angles in the triangle TVW is:

`\[ T + V + W = 180^\circ \]`

This equation holds true for any valid measurements of the interior angles of a triangle. In this case, when
`\(T = 20^\circ\)`,
`\(V = 25^\circ\)`, and
`\(W = 135^\circ\)`, their sum
`\(T + V + W\) equals \(180^\circ\)`, satisfying the equation for a triangle's interior angles.

Answer 2

If we know the measure of two of the three angles of a triangle, since the sum of the angles in a triangle aways is 180º, we can write the equation for angles a, b and c:

`\begin{gathered} m\angle a=x \\ m\angle b=y \\ m\angle c=z \\ \text{Then,} \\ 180º=x+y+z \end{gathered}`

Let's suppose we know x and y, then z is:

`z=180º-x-y`