Plz help
This is due tonight and I’m literally struggling to complete it all

Problem 10

20 degrees

Explanation: Angle GBE = 20 is shown in the diagram which is adjacent to the angle we want. Recall that the incenter is found by constructing the angle bisectors of a triangle. The angle bisectors cut each angle in half. So angle ABG and angle GBE are the same measure.

Problem 11

22 degrees

Explanation: We'll use similar reasoning as above to find that angle GCA is 11 degrees. So angle BCA = (angle BCG)+(angle GCA) = 11+11 = 22.

Problem 12

118 degrees

Explanation: Make a copy of triangle ABC. Ignore the other line segments inside the triangle. We found so far that angle B = 20+20 = 40 degrees and angle C is 22 degrees. Solve A+B+C = 180 to get A = 118. This is the measure of angle BAC.

Problem 13

59

Explanation: Cut the result of problem 12 in half. We're using the same idea as problem 1. Segment AG cuts angle BAC into two equal halves.

Problem 14

4

Explanation: We can show that triangles GEB and GDB are congruent by the AAS congruence theorem. Note the two pairs of congruent angles, and the pair of congruent sides that are not between the angles. From there, we see the corresponding pieces GE and GD are the same length. The diagram shows GE = 4, so GD = 4 also.

Problem 15

11

Explanation: Same idea as problem 14. This time we focus on the corresponding congruent parts BD and BE, which are both 11 units long.

Problem 16

sqrt(137)

Explanation: Focus on triangle GDB or triangle GEB (they're the same triangle, just one is a mirror reflection of the other). Use the pythagorean theorem with a = 4, b = 11 to find that c = sqrt(137)

Problem 17

4*sqrt(26)

Explanation: We'll use a similar idea as problem 14. We can prove triangles GFC and GEC are congruent by AAS. Consequently, we know that FC = EC = 20. The diagram shows EG = 4. Focus on triangle GEC. Use the pythagorean theorem to find that GC = sqrt(416) = 4*sqrt(26)

37

step-by-step explanation: