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 =
°
~~~~~~~~~~~~~~~~


<pre>
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.


<U>ANSWER</U>.  x= 20° ;  m (∠2) = 60°.
</pre>

Solved.


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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Angles/Angles-basics.lesson>Angles basics</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Angles/Vertical-Angles-.lesson>Vertical angles</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/How-to-solve-problems-on-suppl-compl-or-vertical-angles-Examples.lesson>HOW TO solve problems on supplementary, complementary or vertical angles - Examples</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-supplementary-and-complementary-angles-and-pairs-of-angles.lesson>Solved problems on supplementary and complementary angles</A>
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