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1 year ago

If m∠2 = 41°, m∠5 = 94°, and m∠10 = 109°, find each measure.

Mathematics

1 answer:

Orlov [11]1 year ago

8 0

Answer:

Step-by-step explanation:

It's given in this question,

m∠2 = 41°, m∠5 = 94° and m∠10 = 109°

Since, ∠2 ≅ ∠9 [Alternate interior angles]

m∠2 = m∠9 = 41°

m∠8 + m∠9 + m∠10 = 180° [Sum of angles at a point of a line]

m∠8 + 41 + 109 = 180

m∠8 = 180 - 150

m∠8 = 30°

Since, m∠2 + m∠7 + m∠8 = 180° [Sum of interior angles of a triangle]

41 + m∠7 + 30 = 180

m∠7 = 180 - 71

m∠7 = 109°

m∠6 + m∠7 = 180° [linear pair of angles]

m∠6 + 109 = 180

m∠6 = 180 - 109

= 71°

Since m∠5 + m∠4 = 180° [linear pair of angles]

m∠4 + 94 = 180

m∠4 = 180 - 94

m∠4 = 86°

Since, m∠4 + m∠3 + m∠9 = 180° [Sum of interior angles of a triangle]

86 + m∠3 + 41 = 180

m∠3 = 180 - 127

m∠3 = 53°

m∠1 + m∠2 + m∠3 = 180° [Angles on a point of a line]

m∠1 + 41 + 53 = 180

m∠1 = 180 - 94

m∠1 = 86°

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Elsie bought a video game for $85.00. If the store charges 170% of its cost for the game, how much is the store’s profit?

MissTica

Answer: $144.50

Step-by-step explanation:

is/of = %/100

x/85 = 170/100

14,450 = 100x

divide by 100

x = $144.50

6 0

1 year ago

*NO 194 39% 13:08 Pilih jawaban yang paling tepat Segitiga PQR dan segitiga XYZ 5 poin merupakan dua segitiga yang kongruen. Bes

Illusion [34]

Answer:

Option d. PQ = YZ

Step-by-step explanation:

The question in English is

Choose the most appropriate answer. The PQR triangle and the XYZ triangle are two congruent triangles. The angle P = the angle Y and PR = YX. Side pairs of the same length are ... a. PQ = XZ b. QR = YZ c. QR = XY d. PQ = YZ

we know that

If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent

Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement

we have that

$m\angle P=m\angle Y$

$PR=YX$

Triangle PQR is congruent with Triangle YZX

That means

Corresponding angles

$m\angle P=m\angle Y$

$m\angle Q=m\angle Z$

$m\angle R=m\angle X$

Corresponding sides

$PQ=YZ\\QR=ZX\\PR=YX$

8 0

1 year ago

Would apreciate if someone helped me..

PtichkaEL [24]

Answer:

a). x = 11

b). m∠DMC = 39°

c). m∠MAD = 66°

d). m∠ADM = 36°

e). m∠ADC = 18°

Step-by-step explanation:

a). In the figure attached,

m∠AMC = 3x + 6

and m∠DMC = 6x - 49

Since "in-center" of a triangle is a points where the bisectors of internal angles meet.

Therefore, MC is the angle bisector of angle AMD.

and m∠AMC ≅ m∠DMC

3x + 6 = 8x - 49

8x - 3x = 49 + 6

5x = 55

x = 11

b). m∠DMC = 8x - 49

= (8 × 11) - 49

= 88 - 49

= 39°

c). m∠MAD = 2(m∠DAC)

= 2(30)°

= 60°

d). Since, m∠AMD + m∠ADM + m∠MAD = 180°

2(39)° + m∠ADM + 66° = 180°

78° + m∠ADM + 66° = 180°

m∠ADM = 180° - 144°

= 36°

e). m∠ADC = $\frac{1}{2}(m\angle ADM)$

= $\frac{1}{2}(36)$

= 18°

5 0

1 year ago

The vertices of rhombus defg are d(1, 4), e(4, 0), f(1, –4), and g(–2, 0). what is the perimeter of the rhombus?

Harman [31]

Answer: 20 unit.

Step-by-step explanation:

Since, Here the vertices of the rhombus defg are d(1, 4), e(4, 0), f(1, –4), and g(–2, 0).

Where, de, ef, fg, gd are sides of the rhombus defg.

By the distance formula,

$de = \sqrt{(4-1)^2+(0-4)^2}$

$=\sqrt{3^2+4^2}$

$=\sqrt{9+16}$

$=\sqrt{25}$

$= 5$

Thus, the side of rhombus = 5

By the property of rhombus,

de = ef = fg = gd = 5 unit.

Thus, the perimeter of the given rhombus defg = de + ef + fg + gd = 5+5+5+5 = 20 unit

6 0

1 year ago

Read 2 more answers

Ms. Hamby gave a quiz. Two students’ work and the answer key are shown. Ms. Hamby accepts equivalent answers in any form.

Luden [163]

Answer:

Student A and Student B both answered 2 questions correctly.

See explanation below

Step-by-step explanation:

Note: that answers in the form:

$\frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$

ARE ALL EQUIVALENT.

First of all, 4/5 is equivalent to 0.8 if we do long division.

and 19/20 is 0.95 if we do long division.

Now, Student A:

Both of the fractions are correct and the negative sign is equivalent and makes the answer correct, so both are correct.

For Student B:

Similarly, both answers are correct for this student as well, looking at the equivalence we showed first.

Also, "-" (negative) in front of the parenthesis and inside parenthesis here doesn't matter.

Hence,

Student A and Student B both answered 2 questions correctly.

5 0

1 year ago