BOIS PLEASE HELP ME HELP

measure of angle 4 is 140°

measure of angle 1 is 140° (given)

measure of angle 3 is 40°

measure of angle 2 is 40°

Step-by-step explanation:

We're given that one angle is equal to the measure of 140° (we'll make this one be angle 1)

because of vertical angles theorem, which states that angles that are opposite to each other and are formed by two intersecting lines will be congruent.

So that means that measure of angle 4 will also be 140°

Because of vertical angles theorem, that means that <3 is ≅ to <2 (we can make them be x)

The sum of all the angles will equal to 360° (since it's a full angle)

Here's the equation:

140+140+x+x=360

simplify

280+2x=360

2x=80

x=40°

Which means that <3 and <2 both equal 40°

Hope this helps!

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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