Answer:
Step-by-step explanation:
G is the incenter of ΔABC,
Incenter of a triangle is defined by the point where angle bisectors of the interior angles intersect.
10). m∠ABG = m∠CBG = 25°
11). m∠BCG = m∠ACG = 18°
Therefore, m∠BCA = m∠BCG + m∠ACG = 2×18° = 36°
12). m∠ABC + m∠BAC + m∠ACB = 180°
2(25)° + m∠BAC + 36° = 180°
m∠BAC = 180° - 86° = 94°
13). m∠BAG = [tex]\frac{1}{2}[/tex](m∠BAC) = 47°
14). Since, incenter is equidistant from all sides of the triangle,
Therefore, DG = GF = FE = 4 units
15). In right triangle BEG,
tan(25)° = [tex]\frac{\text{GE}}{\text{BE}}[/tex]
BE = [tex]\frac{\text{GE}}{\text{tan}25}[/tex]
= [tex]\frac{4}{\text{tan}25}[/tex]
BE = 8.6
16). In right triangle BEG,
cos(25)° = [tex]\frac{\text{4}}{\text{BG}}[/tex]
BG = [tex]\frac{4}{\text{cos}25}[/tex] = 4.4
17). In right triangle GEC,
sin(18)° = [tex]\frac{\text{GE}}{\text{GC}}[/tex]
GC = [tex]\frac{\text{4}}{\text{sin}(18)}[/tex] = 12.9
