Question

1. in \\( \triangle a b c, \angle a \\) and \\( \angle c \\) are congruent, and the measure of \\( \angle b \\) is \\( 143.6 ^ { \circ } \\). what is the measure of \\( \angle a \\)?

f. \\( 18.2 ^ { \circ } \\)
g. \\( 36.4 ^ { \circ } \\)
h. \\( 71.8 ^ { \circ } \\)
j. \\( 143.6 ^ { \circ } \\)

1. which of the following expressions is equivalent to \\( x ^ { 2 } - x - 30 \\)?

a. \\( ( x + 3 ) ( x - 10 ) \\)
b. \\( ( x + 6 ) ( x - 5 ) \\)
c. \\( ( x - 6 ) ( x + 5 ) \\)
d. \\( ( x - 15 ) ( x - 15 ) \\)

1. which of the following matrices is equal to \\( 5 \left \

$$\begin{array} { c c } { - 4 } & { 2 } \\ { 0 } & { - 5 } \\end{array}$$

\
ight \\)?
f. \\( - 20 - 15 \\)
g. \\( \left \

$$\begin{array} { c } { - 10 } \\ { - 25 } \\end{array}$$

\
ight \\)
h. \\( \left \

$$\begin{array} { l l } { 1 } & { 7 } \\ { 5 } & { 0 } \\end{array}$$

\
ight \\)
j. \\( \left \

$$\begin{array} { c c } { - 20 } & { 10 } \\ { 0 } & { - 25 } \\end{array}$$

\
ight \\)

Explanation:

Step1: Triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle A=\angle C = x\). Then \(x + x+143.6^{\circ}=180^{\circ}\).

Step2: Simplify the equation

Combine like - terms: \(2x=180^{\circ}- 143.6^{\circ}\). So \(2x = 36.4^{\circ}\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{36.4^{\circ}}{2}=18.2^{\circ}\).

Step1: Expand the options

For option B: \((x + 6)(x - 5)=x^{2}-5x+6x - 30\).

Step2: Combine like - terms

\(x^{2}-5x+6x - 30=x^{2}+x - 30\).

Step1: Scalar multiplication of a matrix

If \(A=

$$\begin{bmatrix}a&b\\c&d\end{bmatrix}$$

\) and \(k\) is a scalar, then \(kA=

$$\begin{bmatrix}ka&kb\\kc&kd\end{bmatrix}$$

\). Here \(k = 5\), \(a=-4\), \(b = 2\), \(c = 0\), \(d=-5\).

Step2: Calculate each element

\(5\times(-4)=-20\), \(5\times2 = 10\), \(5\times0=0\), \(5\times(-5)=-25\). So \(5

$$\begin{bmatrix}-4&2\\0&-5\end{bmatrix}$$

=

$$\begin{bmatrix}-20&10\\0&-25\end{bmatrix}$$

\).

Answer:

F. \(18.2^{\circ}\)