Answer:
Part 1) [tex]m \angle G=121^o[/tex]
Part 2) [tex]m \angle BAD=110^o[/tex]
Step-by-step explanation:
Part 1) What is m∠G ?
we know that
The sum of the interior angles in a triangle must be equal to 180 degrees
In the triangle FGH
[tex]m \angle F+m \angle G+m \angle H=180^o[/tex]
substitute the given values
[tex](x-5)^o+(3x+25)^o+x^o=180^o[/tex]
solve for x
[tex]5x+20=180[/tex]
[tex]5x=160[/tex]
[tex]x=32^o[/tex]
Find the measure of angle G
[tex]m \angle G=(3x+25)^o[/tex]
substitute the value of x
[tex]m \angle G=(3(32)+25)=121^o[/tex]
Part 2) What is m∠BAD?
we know that
The Exterior Angle Theorem states that: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
so
[tex]m \angle BAD=85^o+25^o[/tex]
[tex]m \angle BAD=110^o[/tex]
