Mathematics, 07.10.2019 02:00 darkcrystal463

Straight angles are extremely important in geometry. when two lines intersect , they form multiple angles. in the diagram below, line gm and fh intersect at e. if any of the four angles formed is given, all other three can be found quickly. fill in the table below.

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Answer from: manny2085

When two straight lines intersect, the vertical opposite angles intersect. the other two angles are also equal. Let the known angle be x, then the other two adjacent angles are obtained subtracting twice of x from 360 and dividing the result by 2.

Therefore, the table can by filled as follows:

Row 1:

Given <GEF = 120°

<FEM is adjacent to <GEF, thus
$\angle FEM= \frac{360-2(120)}{2} \\ \\ = \frac{360-240}{2} = \frac{120}{2} =60^o$

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <MEH = 120°

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 60°.

Row 2:

Given <MEH = 150°

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 150°

<FEM is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(25)}{2} \\ \\ = \frac{360-50}{2} = \frac{310}{2} =155^o$

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 30°.

Row 3:

Given that <FEM = 25°

<FEM is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(25)}{2} \\ \\ = \frac{360-50}{2} = \frac{310}{2} =155^o$

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 155°

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 25°.

Row 4:

Given that <HEG = 45°

<HEG is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(45)}{2} \\ \\ = \frac{360-90}{2} = \frac{270}{2} =135^o$

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <FEM = 45°

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 135°.

Answer from: Quest

details

step-by-step explanation:

Answer from: Quest

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

$a=9\times 12=108\text {ft^2}$

so the area of the floor is 108 square feet, converting that into square yards we get,

$108 \times 0.1111= 12 \text{yd^2}$

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

$\$15 \times 12=\$180$

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

$a = 12 \times 15=180\text {ft}^2$

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

$180 \times 0.111=20 \text {yd}^2$

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

$\$15 \times 20= \$300$

so, it will cost $300.

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