Question

1. classify the triangle by its sides. 11) calculate the measure of each angle of an equilateral triangle. a) (1-2) - b) (14) - 180° = 25.20 11.25 12) suppose the polygon is regular. use the formula to calculate its exterior angle. 180/n = 16 16 13) what is the sum of the measures of the angles? 14) what is the measure of each exterior angle of a regular octagon (8-sided polygon) to the nearest whole degree? learning target: i can apply properties, postulates, and theorems with parallel lines and congruent triangles. score: 13) complete the proof. given: ta = xz prove: yz = ac statements reasons 1) y a = x z 1) given 2) 2) vertical angles 3) asa 4) 4) cpctc

Explanation:

To solve the problems related to triangles (interior angles, regular polygons, congruent triangles), we'll address each sub - question:

10) a) Calculate the sum of interior angles of a polygon

The formula for the sum of interior angles of a polygon with \(n\) sides is \((n - 2)\times180^{\circ}\).
For a triangle, \(n = 3\).

Step 1: Substitute \(n = 3\) into the formula

\((3-2)\times180^{\circ}\)

Step 2: Simplify the expression

\(1\times180^{\circ}=180^{\circ}\)

Answer:

\(180^{\circ}\)

10) b) Calculate the measure of each interior angle of a regular \(n\) - gon

The formula for the measure of each interior angle of a regular \(n\) - gon is \(\frac{(n - 2)\times180^{\circ}}{n}\).
Given \(n = 15\) (from the hand - written \(180/15 = 12\), maybe a typo, but let's assume \(n = 15\) for the formula application).

Step 1: Substitute \(n = 15\) into the formula

\(\frac{(15 - 2)\times180^{\circ}}{15}\)

Step 2: Simplify the numerator

\((15 - 2)\times180^{\circ}=13\times180^{\circ}=2340^{\circ}\)

Step 3: Divide by \(n = 15\)

\(\frac{2340^{\circ}}{15}=156^{\circ}\) (If we take the hand - written \(180/n\) with \(n = 16\) (as in the image \(180\div16 = 11.25\), but that might be a different polygon). If \(n = 16\), \(\frac{(16 - 2)\times180^{\circ}}{16}=\frac{14\times180^{\circ}}{16}=\frac{2520^{\circ}}{16}=157.5^{\circ}\), but the hand - written \(180\div16 = 11.25\) is wrong. Correctly, for a regular \(n\) - gon, it's \(\frac{(n - 2)\times180^{\circ}}{n}\))

11) What is the sum of the interior angles of a 20 - gon?

Using the formula \((n - 2)\times180^{\circ}\) with \(n = 20\).

Step 1: Substitute \(n = 20\) into the formula

\((20 - 2)\times180^{\circ}\)

Step 2: Simplify the expression

\(18\times180^{\circ}=3240^{\circ}\)