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Question 1191304: Use the drawing in which
AC intersects DB
at point O to answer the question.
Two lines intersect at point O to form four angles.
Line A C goes from point A in the top left, through point O in the center, to point C in the bottom right.
Line D B goes from point D in the bottom left, through O on line A C, to point B in the top right.
The angle at the bottom, ∠C O D, is labeled 1.
The angle on the left, ∠D O A, is labeled 2.
The angle at the top, ∠A O B, is labeled 3.
The angle on the right, ∠B O C, is labeled 4.
If
m∠2 = (x + 40)°
and
m∠3 = (3x)°,
find x and m∠2 in degrees.
x =
m∠2 =
°
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
Use the drawing in which
AC intersects DB
at point O to answer the question.
Two lines intersect at point O to form four angles.
Line A C goes from point A in the top left, through point O in the center, to point C in the bottom right.
Line D B goes from point D in the bottom left, through O on line A C, to point B in the top right.
The angle at the bottom, ∠C O D, is labeled 1.
The angle on the left, ∠D O A, is labeled 2.
The angle at the top, ∠A O B, is labeled 3.
The angle on the right, ∠B O C, is labeled 4.
If
m∠2 = (x + 40)°
and
m∠3 = (3x)°,
find x and m∠2 in degrees.
x =
m∠2 =
°
~~~~~~~~~~~~~~~~
Make a sketch.
Angle 2 (DOA) and angle 3 (AOB) are supplementary angles: they sum up to 180°.
So we write this equation
x + 40 = 3x degrees.
Simplify this equation and find x
40 = 3x - x
40 = 2x
x = 40/2 = 20 degrees.
Thus we just found x= 20 degrees.
Hence, m (∠2) = x + 40 = 20 + 40 = 60 degrees.
ANSWER. x= 20° ; m (∠2) = 60°.
Solved.
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To learn about supplementary angles, read the lessons
- Angles basics
- Vertical angles
- HOW TO solve problems on supplementary, complementary or vertical angles - Examples
- Solved problems on supplementary and complementary angles
in this site.
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