The measure of the following angles are below;
- m∠ABG = 20°
- m∠BCA = 22°
- m∠BAC = 118°
- m∠BAG = 59°
What is the measure of the angles?
m∠CBG = 20°, m∠BCG = 11°
The incenter of a triangle is the point where the three bisectors of ΔABC meets
So,
m∠ABG = m∠CBG = 20° (definition of angle bisector)
m∠ABG = 20°
m∠ACG = m∠BCG = 11° (definition of angle bisector)
m∠ACG = 11°
m∠BCA = m∠ACG + m∠BCG
= 11° + 11°
= 22°
m∠ABC = m∠ABG + m∠CBG
= 20° + 20°
= 40°
m∠BAC = 180° - (m∠BCA+m∠ABC) complementary angles
= 180° - (40° + 22°)
= 118°
m∠BAG = m∠CAG (definition of angle bisector)
m∠BAC = 118°
= m∠BAG + m∠CAG
= m∠BAG + m∠BAG
= 2 × m∠BAG
2 × mBAG = 118°
m∠BAG = 118°/2
= 59°
m∠BAG = 59°