Answer:
Step-by-step explanation:
A) Find the figure attached. According to the figure, since line PQ is parallel to line RS, then <CBQ = <DCS (corresponding angle)
Also <BCS + <DCS = 180° (sum of angles on a straight line)
Given
<BCS = (5a+14)° and <DCS = <CBQ =(2a-9)°
Substituting this values into the formula to calculate the value of a;
(5a+14)°+(2a-9)° = 180°
5a+2a+14-9 = 180
7a+5 = 180
7a = 180-5
7a = 175
a = 175/7
a = 25°
Hence the value of a is 25°
B) From the diagram <ABQ = <BCS = 5a+14 (corresponding angle)
Substitute a = 25 into the expression
<ABQ = 5(25)+14
<ABQ = 125+14
<ABQ = 139°
C) To get <BCR, we will use the formula;
<BCR + <BCS = 180
Given <ABQ = <BCS = 139°
<BCR = 180 - <BCS
<BCR = 180 - 139
<BCR = 41°
