In the figure below ABCDE is the roof of a house, GB parellel FD and Angle ACE is equal to 106 degree . Find the angle x
Answers
Step-by-step explanation:
sorry bro I don't know hope you will understand
Given : ABCDE is the roof of a house
GB||FD and ∠ACE= 106°
https://brainly.in/question/48076348 for figure
To Find : ∠x
Solution:
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent. ( Equal in Measure)
• Alternate angles are congruent. ( Interiors & Exterior both )
• Co-Interior angles are supplementary. ( adds up to 180°)
Method 1 :
Draw a line CP || GB and FD
∠BCP = ∠x and ∠DCP = ∠x corresponding angles
∠BCP + ∠DCP = ∠BCD = ∠ACE
=> ∠BCP + ∠DCP = 106°
=> x + x = 106°
=> 2x = 106°
=> x = 53°
Hence ∠x is 53°
Another method :
Sum of angles of a pentagon is 540°
∠BGF + ∠DFG = 180° Supplementary angles
∠GBC = 180° - x linear pair
∠FFC = 180° - x linear pair
=> ∠BGF + ∠DFG + ∠GBC + ∠FFC + ∠BCD = 540°
∠BCD = ∠ACE = 106°
=> 180° + 180° - x + 180° - x + 106° = 540°
=> 2x = 106°
=> x = 53°
Hence ∠x is 53°
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