6. Find the area of the shaded region. All angles are right angles. Show your reasoning.
35
10
15
10
30
10
15
10
60

  1400 square units

Step-by-step explanation:

The area can be computed by subtracting the areas of the white rectangles at three corners from the overall 60×30 rectangle.

The upper left corner white space is 10×10 = 100 square units.

The upper right and lower left white spaces are 15×10 = 150 square units each.

Then the shaded area is ...

  60×30 -100 -2(150) = 1800 -100 -300 = 1400 . . . square units

Alternate solution

You can extend each of the horizontal edges across the figure to divide it into three rectangles. From the top down, these have dimensions and areas of ...

  35×10 +60×10 +45×10 = 10(35+60+45) = 10(140) = 1400 . . . square units

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Area of a rectangle is the product of length and width.

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.