Question

PLEASE HELP ME !!!
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Answer 1

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 =
`(1)/(2)`(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)° =
`\frac{\text{GE}}{\text{BE}}`

BE =
`\frac{\text{GE}}{\text{tan}25}`

=
`\frac{4}{\text{tan}25}`

BE = 8.6

16). In right triangle BEG,

cos(25)° =
`\frac{\text{4}}{\text{BG}}`

BG =
`\frac{4}{\text{cos}25}` = 4.4

17). In right triangle GEC,

sin(18)° =
`\frac{\text{GE}}{\text{GC}}`

GC =
`\frac{\text{4}}{\text{sin}(18)}` = 12.9