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9 days ago

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Origami is the Japanese art of paper folding. The diagram below represents an unfolded paper kabuto, a samurai warrior's helmet.

From the kabuto below, which of the following are pairs of congruent angles?

2 answers:

PIT_PIT [9.1K]9 days ago

8 0

Congruent angles have the same measurement.

Let’s evaluate the provided pairs one by one.

A. ∠MKR and ∠OAR

In the diagram, it’s visible that the angle bisector of the right-angled vertices creates angles MKR and OAR.

Thus, they are congruent measuring 45°

B. ∠ONT and ∠MTN

From the diagram, MTN forms a right angle, while ONT is created by bisecting this right angle.

Hence, these angles are not congruent with ∠MTN at 90° and ∠ONT at 45°

C. ∠IRS and ∠MRO

In the diagram, MRO is a right-angle, while IRS results from the bisection of the right angle.

Accordingly, these angles are not congruent with ∠MRO equal to 90° and ∠IRS at 45°

D. ∠URC and ∠TRO

In the diagram, it’s shown that the angle bisector of the right-angled vertices forms angles URC and TRO.

Thus, they are congruent, both measuring 45°

Therefore, the pairs of congruent angles are

A. ∠MKR and ∠OAR and D. ∠URC and ∠TRO

tester [8.8K]9 days ago

3 0

Response:

a and d

Detailed explanation:

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The equation that represents the canned goods order is 24x + 64y = 384, where x = number of minutes for producing fruit cans and

PIT_PIT [9117]

Answer:

The y-intercept represents the number of minutes allocated for creating vegetable cans when no time is dedicated to fruit cans.

Step-by-step explanation:

The problem indicates that y refers to the minutes spent on vegetable can production, and the y-intercept indicates the y-value where x equals zero.

Thus, the y-intercept signifies the duration for producing vegetable cans when no time has been utilized for fruit can production.

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1 month ago

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If m<DBC=(12x-3)°, m<DBE=(5x+12)°, and m<EBC=(3x+13)°, find m<EBC.

Leona [9271]

Answer:

m∠EBC=34°

Step-by-step explanation:

We establish that

m∠DBC=m∠DBE+m∠EBC

Refer to the accompanying diagram for clarity on the issue

Replace the known values in the equation and determine x

$(12x-3)\°=(5x+12)\°+(3x+13)\°\\12x-3=8x+25\\12x-8x=25+3\\4x=28\\x=7$

Calculate the size of angle EBC

m∠EBC=(3x+13)°

Insert the value for x

m∠EBC=(3(7)+13)°

m∠EBC=(21+13)°

m∠EBC=34°

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1 month ago

∠UVW and ∠XYZ are complementary angles, m∠UVW=(x−10)º , and m∠XYZ=(4x−10)º .

lawyer [9240]

We recognize that two angles, ∠UVW and ∠XYZ, are complementary, which means their sum is 90°.

Their measures are given as:

∠UVW = x - 10

∠XYZ = 4x - 10

Adding these, we have:

(x - 10) + (4x - 10) = 90

Simplifying:

5x - 20 = 90

Adding 20 to both sides:

5x = 110

Dividing by 5:

x = 22

Substituting back:

∠UVW = 22 - 10 = 12°

∠XYZ = 4(22) - 10 = 78°

Therefore, the values are:

x = 22°

∠UVW = 12°

∠XYZ = 78°

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1 month ago

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Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =

tester [8842]

Answer:

Attached is the question in consideration.

$m\angle CEA =90 \ (deg)$

$m\angle BEF=135\ (deg)$

$\angle CEF$ forms a straight line.

$\angle AEF$ depicts a right triangle.

The options $1,4,5,6$ represent the correct answers.

Step-by-step explanation:

⇒ Given that $\ ray\ AE$ is ⊥ $FEC$ it constitutes a right triangle, leading to $m\angle CEA =90\ (deg)$ .

⇒ The measure for $\angle BEF =135\ (deg)$ equals $\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)$ as $\angle AEB$ bisects $\angle AEC$ , implying that $\angle AEB$ is half of $\angle AEC$ , thus $\angle AEB = 45\ (deg)$ .

⇒ $\angle CEF$ represents a straight line, as the angle measures across it yield $180\ (deg)$ .

⇒ The angle measure for $\angle AEF = 90\ (deg)$ is derived from the linear pair concept.

Since $\angle CEA + \angle AEF = 180\ (deg)$ , inserting the values of $m\angle CEA =90\ (deg)$ leads to $\angle AEF = 90\ (deg)$ .

The other two options are incorrect as:

$m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225$

it surpasses $180\ (deg)$ while $\angle CEF$ is a

straight line.

Also, $m\angle CEB=2(m\angle CEA)$ is inaccurate.

As $\angle CEA = 90\ (deg)$ and $\angle CEB=45\ (deg)$

Thus, we have a total $4$ valid answers.

The confirmed options are $1,4,5,6$ .

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In which diagram are angles 1 and 2 vertical angles?

PIT_PIT [9117]

Response

The first diagram displays angles 1 and 2 as vertical angles.

Clarification

In all four diagrams, the initial one illustrates the vertically opposite angles.

Angles 1 and 2 are classified as vertically opposite because they face each other.

These angles maintain equal measurement when two lines intersect, resulting in four angles where two pairs of vertically opposite angles are formed.

In contrast, all other figures depict angles 1 and 2 as adjacent angles.

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21 day ago

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