The image shown has two triangles sharing a vertex:

Mathematics

2 answers:

Vika [28.1K]3 years ago

8 0

Answer:

40°.

Step-by-step explanation:

We can see from the diagram (in the comments) that ∠UWV and ∠XWZ are vertical angles; this is because they are opposite angles that share only a vertex.

We can also see that both of these angles are 90°.

This gives us two angle measures of triangle WXZ, 50 and 90. We know that the sum of the measures of the angles of a triangle is 180°; this gives us

180-(50+90) = 180-140 = 40° for the angle.

ZanzabumX [31]3 years ago

6 0

So you know that the sum of angles in a triangle is 180°.
You know two of the angles in triangle WXZ. The two angles are angle WXZ, which is 50° and angle XWZ, which is 90°.

Now you can calculate angle WZX, by:
180-50-90=40°.

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The outside diameter of the igloo is 12 feet. The thickness of each block of ice that was used to construct the igloo is 1.5 fee

mojhsa [17]

The first thing we are going to do for this case is to model the igloo as a hemisphere.
The volume of the hemisphere is:
V = ((4/3) * (pi) * (r ^ 3)) / 2
Where,
r: sphere radio
We have then that the internal diameter is:
di = 12-1.5
di = 10.5 feet
So the radio is:
r = di / 2
r = 10.5 / 2
r = 5.25 feet
Substituting values:
V = ((4/3) * (pi) * ((5.25) ^ 3)) / 2
V = 303.1 feet ^ 3
Answer:
the amount of space of the living area inside the igloo is:
V = 303.1 feet ^ 3

6 0

3 years ago

Given quadrilateral TUVX ~ quadrilateral MNOP and VX = 5, XT = 10, and OP = 7, what is PM?

Likurg_2 [28]

$\dfrac{\overline{PM}}{\overline{OP}}=\dfrac{\overline{XT}}{\overline{VX}}\\\\
\dfrac{\overline{PM}}{7}=\dfrac{10}{5}\\\\
\dfrac{\overline{PM}}{7}=2\\\\
\overline{PM}=14$