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What is the measure of the exterior angle x

? (1 point)
top is 37
botoom is 42

11 answers

To find the measure of the exterior angle \( x \), we first need to relate it to the interior angles. An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

In this case, if the angles given are the interior angles of a triangle, we have:

  • One angle = 37 degrees
  • Another angle = 42 degrees

To find the third angle of the triangle, we use the fact that the sum of the interior angles of a triangle is always 180 degrees:

\[ \text{Third angle} = 180 - (37 + 42) = 180 - 79 = 101 \text{ degrees} \]

Now, the exterior angle \( x \) that corresponds to the 101-degree angle is:

\[ x = 101 \text{ degrees} \]

Thus, the measure of the exterior angle \( x \) is 101 degrees.

Use the figure to answer the question.

A rightward inclined transversal passes through two horizontal parallel lines labeled upper S and upper T. Angles formed at the intersection point of line upper S are labeled clockwise from the top: 1, 2, 4, and 3. Corresponding angles formed at the intersection point of line upper N are labeled clockwise from the top: 5, 22 degrees, 7, and 6.

In the picture, one angle is labeled 22°
and lines S
and T
are parallel. Which other three angles will be 22°
? Separate each angle number with a comma.

(1 point)
angles
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Given that lines S and T are parallel and a transversal intersects them, corresponding angles are equal, and alternate interior angles are equal as well.

You mentioned one angle is labeled 22° at the intersection with line T. In this scenario, since angles 5, 6, 7, and 22° are mentioned at the intersection of line N, we can establish the relationships:

  1. Angle 2 (above angle 22°) is a corresponding angle to angle 5, so:

    • Angle 2 = 22°

  2. Angle 4 (the angle vertically opposite to angle 22° at the intersection with line S) is also equal, so:

    • Angle 4 = 22°

  3. Angle 6 (the angle to the left of angle 22°) is also vertical opposite to angle 3, therefore:

    • Angle 6 = 22°

So, the three angles that will also measure 22° are the following:

Angles: 2, 4, 6.

What is the supplement of an angle that measures 77°
?(1 point)
Responses

The supplement of the angle is 77°
because supplementary angles are congruent.
The supplement of the angle is 77 degrees because supplementary angles are congruent.

The supplement of the angle is 13°
because 90°−77°=13°
.
The supplement of the angle is 13 degrees because 90 degrees minus 77 degrees equals 13 degrees .

The supplement of the angle is −103°
because 77°−180°=−103°
.
The supplement of the angle is negative 103 degrees because 77 degrees minus 180 degrees equals negative 103 degrees .

The supplement is 103°
because 180°−77°=103°
.

The supplement of an angle is found by subtracting the angle from 180 degrees.

Given that the angle measures 77°, the calculation for its supplement is as follows:

\[ \text{Supplement} = 180° - 77° = 103° \]

Therefore, the correct response is:

The supplement is 103° because 180° − 77° = 103°.

Use the image to answer the question.

An illustration shows two school crossing signs labeled Figure A and Figure B. The signs are pentagons. A silhouette of a walking man and woman are centrally located on the signs. Starting at the bottom left vertex of both figures, the vertices are labeled A, B, C, D, and E. A line inside Figure A connects the vertices B and D. A vertical perpendicular line extends down from the top vertex C to the base side A E. Lines inside Figure B connect the vertices A and C, B and D, and C and E.

Select the correct decomposition into triangles of the sign shaped as a pentagon.

Choose 1 for Figure A
, 2 for Figure B
, or 3 for both Figure A
and Figure B
.

(1 point)
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To determine the correct decomposition into triangles for the pentagonal figures, we must analyze the connections mentioned:

  1. Figure A: You mentioned that a line connects vertices B and D, and a vertical perpendicular line extends from C to line AE. This suggests that Figure A is being divided successfully into triangles by forming segments that connect non-adjacent vertices.

  2. Figure B: In this figure, it was stated that lines connect vertices A and C, B and D, and C and E. This decomposition also leads to multiple triangles being formed.

Since both figures A and B have their respective lines that connect vertices to form triangles, the correct decomposition into triangles can be attributed to both figures.

Therefore, the correct answer would be:

3 for both Figure A and Figure B.

Use the image to answer the question.

An illustration of a hendecagon with the vertices labeled upper A, upper B, upper C, upper D, upper E, upper F, upper G, upper H, upper I, upper J, and upper K clockwise from the top.

Find the sum of the interior angles of a hendecagon (11-sided polygon).

(1 point)
The sum of the interior angles of a hendecagon is
°
.
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To calculate the sum of the interior angles of a polygon, you can use the formula:

\[ \text{Sum of interior angles} = (n - 2) \times 180° \]

where \( n \) is the number of sides of the polygon.

For a hendecagon, which has 11 sides:

\[ \text{Sum of interior angles} = (11 - 2) \times 180° = 9 \times 180° = 1620° \]

Therefore, the sum of the interior angles of a hendecagon is 1620°.

If triangle DEF
has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point)

To determine whether triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can use the Pythagorean theorem. According to the theorem, a triangle is a right triangle if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides.

Let's identify the sides of the triangle:

  • The longest side (hypotenuse) is 50.
  • The other two sides are 40 and 32.

Now we will apply the Pythagorean theorem:

\[ c^2 = a^2 + b^2 \] where \( c \) is the longest side.

Substituting the lengths of the sides:

\[ 50^2 = 40^2 + 32^2 \]

Calculating each term:

\[ 2500 = 1600 + 1024 \] \[ 2500 \neq 2624 \]

Since \( 2500 \neq 2624 \), triangle DEF does not satisfy the Pythagorean theorem and therefore is not a right triangle.

Thus, the answer is:

0.