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Compute angle $x,$ in degrees.

[asy]
unitsize(1 cm);

pair A, B, C, D, E;

A = (2,3);
B = (0,0);
C = (5,0);
D = interp(A,C,1/3);
E = interp(B,C,2/3);

draw(A--B--C--cycle);
draw(D--E);

label("$77^\circ$", A + (0.1,-0.6));
label("$61^\circ$", B + (0.6,0.3));
label("$x$", D + (0.3,-0.6));
label("$105^\circ$", E + (0.4,0.3));
[/asy]

Sagot :

Sqdancefanidn

Answer:

  33°

Step-by-step explanation:

You want the measure of the angle marked x in the attached figure.

Angle sum

The sum of angles in a triangle is 180°. This means ...

  61° +77° + C = 180°

  105° + x + C = 180°

Subtracting the second equation from the first gives ...

  61° +77° -105° -x = 0

  x = 138° -105° = 33°

The angle x is 33°.

__

Additional comment

The drawing is not to scale. For the given grid points, the angles are off by a few degrees in each case. We have assumed the angles have their marked values.

View image Sqdancefan
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