Two lines intersect to form angles 1, 2, 3, and 4 as given. The measure of ∠3 is 38°. What is the measure of ∠2 ?

Mathematics

2 answers:

crimeas [40]3 years ago

8 0

Answer:

142° i think

Step-by-step explanation:

ss7ja [257]3 years ago

3 0

Answer:

142° is the measure of angle 2.

Step-by-step explanation:

When two lines intersect, they make four angles. The angles facing each other are equal.

Let's say that two lines a and b intersected each other to make angles 1,2,3 and 4 respectively.

The measure of angle 3 = 38 degrees.

We know that the angle 1 is against angle 3 and is equal to 38.

Also Angle 2 and Angle 4 are also against each other and are equal let's say equal to x degrees.

Now, the sum of all four angles = 360 degrees

∠1 + ∠2+ ∠3 + ∠4 = 360°

38° + x + 38° + x = 360°

2x = 360° - 76°

2x = 284°

x = 142°

Hence, ∠2 = 142°

You might be interested in

the line joining A(a, 3) to B(2 -3) is perpendicular to the line joining C(10,1) to B. The value of a is?

RideAnS [48]

Well, first off, let's find what is the slope of BC

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
B&({{ 2}}\quad ,&{{ -3}})\quad 
% (c,d)
C&({{ 10}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-3)}{10-2}\implies \cfrac{1+3}{10-2}
\\\\\\
\cfrac{4}{8}\implies \cfrac{1}{2}$

now, a line perpendicular to that one, will have a negative reciprocal slope, thus

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2}\\\\
slope=\cfrac{1}{{{ 2}}}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies \boxed{-2}$

now, we know the slope "m" of AB is -2 then, thus

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ a}}\quad ,&{{ 3}})\quad 
% (c,d)
B&({{ 2}}\quad ,&{{ -3}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-3}{2-a}=\boxed{-2}
\\\\\\
\cfrac{-6}{2-a}=-2\implies -6=-4+2a\implies -2=2a\implies \cfrac{-2}{2}=a
\\\\\\
-1=a$

6 0

3 years ago

Help me plzzzzzzzzzzzzzzzz

irina [24]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

State that dgree of the term -6x²y

vladimir2022 [97]

I think it’s -6 but I would check with someone else too lol