(9)
<em>x</em> ° = 1/2 (130° - 30°) = 50°
(due to a theorem about intersecting secants/tangents)
(11) The labeled angle subtends a minor arc of meaure 120°, which means the larger arc has a measure of 360° - 120° = 240°. Then
<em>x</em> ° = 1/2 (240° - 120°) = 60°
(due to the same theorem)
(13) The labeling here is a bit confusing. I'm not sure what the 70° is referring to. It occurs to me that it might be info from a different exercise, so that <em>y </em>° is the measure of the angle made by the tangent to the circle with a vertex of the pentagon, and <em>x</em> ° is the measure of each arc that passes over an edge of the pentagon.
Each arc makes up 1/5 of the circle's circumferece, so
<em>x</em> ° = 360°/5 = 72°
The pentagon is regular, so each of its interior angles have the same measure of 108°. (Why 108°? Each exterior angle measures 360°/5 = 72°, since the exterior angles sum to 360°. Interior and exterior angles are supplementary, so the interior angles measure 180° - 72° = 108° each.)
The angles formed by the tangent to the circle are supplementary, so that
<em>y</em> ° + 108° + <em>y</em> ° = 180°
2<em>y</em> ° = 72°
<em>y</em> ° = 36°
Answer:
The answer to the question is
The kinds of polygons that could be Diedre's quadrilateral are rectangle and square
Step-by-step explanation:
We note the conditions of the polygon as thus
Number of sides = 4, Which include trapezoid, square, rectangle
Size of angles = 90 ° which eliminates trapezoid
Sizes of opposite sides = Equal opposite sides, includes square and rectangle
With the above we conclude that the possible polygons in Diedre's quadrilateral are rectangle and square
Answer:
13/18
Step-by-step explanation:
- 6.5 · 1/9 = 6 5/10 · 1/9
- 6 5/10 · 1/9 = 6 1/2 · 1/9
- 6 1/2 · 1/9 = 13/2 · 1/9
- 13/2 · 1/9 = 13/18
Therefore, 6.5 · 1/9 = 13/18.
Answer:
Step-by-step explanation:
x-y=11
2x+y=19
---------------
x=y+11
2(y+11)+y=19
2y+22+y=19
3y+22=19
3y=19-22
3y=-3
y=-3/3
y=-1
x-(-1)=11
x+1=11
x=11-1
x=10
Answer: x=10, y=-1. (10, -1).
-----------------------------------------
-6x+5y=1
6x+4y=-10
-------------------
9y=-9
y=-9/9
y=-1
6x+4(-1)=-10
6x-4=-10
6x=-10+4
6x=-6
x=-6/6
x=-1
Answer: x=-1, y=-1. (-1, -1).
------------------------------------
2x+9y=25
-4x-9y=-23
-------------------
-2x=2
x=2/-2
x=-1
2(-1)+9y=25
-2+9y=25
9y=25-(-2)
9y=25+2
9y=27
y=27/9
y=3
Answer: x=-1, y=3. (-1, 3).
