Question

target: i can find interior angle measures of polygons
focus: i can explain how to find the sum of interior angle measures; i can use an equation to find interior
angle measure of a polygon
vocab: polygon, regular polygon
warm up
find the quotient.
-\\( \frac { 42 } { 7 } \\)
solve the
equation for y.
\\( 8 y + 6 x = 7 \\)
\\( \triangle x ^ { \prime } y ^ { \prime } z ^ { \prime } \\) is a
dilation of
\\( \triangle x y z \\). identify
the type of
dilation and find
the scale factor.

Explanation:

Solve the equation for \(y\)

Step1: Subtract \(6x\) from both sides

\(8y+6x - 6x=7 - 6x\)
\(8y=7 - 6x\)

Step2: Divide both sides by \(8\)

\(y=\frac{7 - 6x}{8}\)

Step1: Perform the division

Since \(42\div7 = 6\), and we have a negative sign in front of the fraction.
\(-\frac{42}{7}=-6\)

Step1: Find the lengths of corresponding sides

Let's assume \(XY = 6\) (from \(Y(0,6)\) to \(X(0,0)\)) and \(X'Y'=2\) (from \(Y'(0,2)\) to \(X'(0,0)\))

Step2: Calculate the scale factor

The scale factor \(k=\frac{X'Y'}{XY}=\frac{2}{6}=\frac{1}{3}\)
Since \(k=\frac{1}{3}<1\), it is a reduction.

Answer:

\(y=\frac{7 - 6x}{8}\)

Find the quotient \(-\frac{42}{7}\)