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stich3 [128]
1 year ago
9

Give 1 pair of Vertical and 1 pair of Supplementary angles

Mathematics
1 answer:
mojhsa [17]1 year ago
8 0

Solution:

Vertical angles are a pair of opposite angles formed by intersecting lines. re vertical angles. Vertical angles are always congruent.

These two angles (140° and 40°) are Supplementary Angles because they add up to 180°:

Notice that together they make a straight angle.

Hence,

From the image

The following pairs form vertical angles

\begin{gathered} \angle1=\angle3(vertical\text{ angles)} \\ \angle2=\angle4(vertical\text{ angles)} \\ \angle5=\angle7(vertical\text{ angles)} \\ \angle6=\angle6(vertical\text{ angles)} \end{gathered}

Hence,

One pair of the vertical angles is ∠1 and ∠3

Part B:

Two angles are said to be supplementary when they ad together to give 180°

Hence,

From the image,

The following pairs are supplementary angles

\begin{gathered} \angle5+\angle6=180^0(supplementary\text{ angles)} \\ \angle5+\angle8=180^0(supplementary\text{ angles)} \\ \angle7+\angle8=180^0(supplementary\text{ angles)} \\ \angle6+\angle7=180^0(supplementary\text{ angles)} \\ \angle1+\angle2=180^0(supplementary\text{ angles)} \\ \angle1+\angle4=180^0(supplementary\text{ angles)} \\ \angle2+\angle3=180^0(supplementary\text{ angles)} \\ \angle3+\angle4=180^0(supplementary\text{ angles)} \end{gathered}

Hence,

One pair of supplementary angles is ∠5 and ∠6

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The given matrix equation is,

1.5\left[\begin{array}{cc}x&6\\8&4\end{array}\right] +y\left[\begin{array}{cc}1&4\\3&2\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right].

Multiplying the matrices with the scalars, the given equation becomes,

\left[\begin{array}{cc}1.5x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]  \\

Adding the matrices,

\left[\begin{array}{cc}1.5x+y&9+4y\\12+3y&6+2y\end{array}\right]  =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]  \\

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1.5x+y=z\\ 9+4y=z\\ 12+3y=6z\\ 6+2y=2

Solving the equations together,

y=-2\\ 3y-1.5x=9\\ -1.5x=9+6\\ x=-10

We can see that the equations are not consistent.

There is no solution.

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