Question

17. In the figure given alongside,
AB CD EF BC, CBAC = 60° and
DHF = 50. Find ZGCH and ZAGH.
G
H50
B​

Answer 1

Answer:

• From the given figure we know that BAC and ACD are alternate angles
• so we get BAC=ACD=60°
• so we get
• BAC=GCH=60°
• from the figure we also know that DHF and CGH are vertically opposite angles
• so we get
• DHF=CHG=50°
• we know that the sum of the angles in triangle GCH is 180°
• so we can get it as
• GCH+CHG+CGH=180°
• by substituting the values
• 60°+50° +CGH=180°
• on further calculation by subtraction CGH= 180° - 60°- 50°
• CGH=180°- 110°
• CGH=70°
• from the given figure we know that CGH and AGH from a linear pair of angles
• so we get
• CGH+AGH=180°
• by substituting the values 70° +180°
• on further calculation
• AGH=180°- 70°
• by subtraction AGH=110°
• therefore GCH=60°and AGH=110°