Find the measure of the indicated angle

52°

Step-by-step explanation:

x = 51

Step-by-step explanation:

The triangle is isosceles. The markings tell us that.

The 78 is not opposite either one of the equal sides. Let the angle values opposite the equal sides be x

x + x + 78 = 180                      All triangles = 180

2x + 78 = 180                         Subtract 78 from both sides.

2x = 180 - 78

2x = 102                                 Divide both sides by 2

x = 102/2

x = 51

So x = 51

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4