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Answers
Answer:
6)52.5°
7)60°
8)30°,60° and 90°
9)x=50°, y=77°
10)75
Step-by-step explanation:
6)Let two interior angles be x.
By exterior angle property,
x+x=105°
2x=105°
x=105°/2
x=52.5°
7) Construction:Draw XY line passing through Q and parallel to OP and RS.
PQX+PQR+RQY=180°(angle on a straight line)-----------------------1
AnglePQX+OPQ=180(Co-interior angles)
PQX+110°=180°
PQX=70°---------------2
AngleRQY+QRS=180°
RQY+130°=180°
RQY=50°---------------3
From 1,2&3 ,
70°+PQR+50°=180°
PQR=180°-120°
PQR=60°
8)Let the angles be x ,2x and 3x.
By angle sum property,
x+2x+3x=180°
6x=180°
x=30°
Therefore, angles are 30°, 60° and 90°.
9) 127°=y+50° (alternate interior angle)
y=127-50
y=77°
127°=x+y (exterior angle property)
127°=x+77°
x=127-77
x=50°
10)BAC+ACD=180°( Co-interior angle)
75°+ACD=180°
ACD=180°-75°
ACD=105°
105=x+30°(exterior angle property)
x= 75°