A circle will create 360 degree angle measure. Angle covered by two radii will be lesser than 360 degree.
For each
figure, determine the indicated measures.
Problem 1:
Solution :
measure of arc QS = 180˚ - mST
measure of arc QS = 180˚ - 55˚
measure of arc QS = 125˚
measure of arc RS = 180˚ - m ST - m TU
= 180˚ - 47˚ - 55˚
measure of arc RS = 78˚
measure of arc RQT = 360˚ - measure of arc ST - measure of arc RS
= 360˚ - 55˚ - 78˚
measure of arc RQT = 227˚
Problem 2 :
Solution :
measure of arc HG = 180 - 90˚ - 23˚
measure of arc HG = 67˚
measure of arc FEH = 180˚ + 23˚
m FEH = 203˚
Problem 3 :
Find the value of x.
Solution :
m∠GFH + m∠HFJ + m∠GFJ = 360˚
130˚ + 90˚ + m∠GFJ = 360˚
220˚ = m∠GFJ = 360˚
m∠GFJ = 360˚ - 220˚
m∠GFJ = 140˚
So, value of x is 140˚.
Problem 4 :
Solution :
165˚ + 145˚ + x = 360˚
310˚ + x = 360˚
x = 360˚ - 310˚
x = 50˚
So, value of x is 50˚.
Problem 5 :
Solution :
40˚ + 85˚ + 90˚ + x˚ = 360˚
215˚ + x˚ = 360˚
x = 360˚ - 215˚
x = 145˚
So, value of x is 145˚.
Problem 6 :
i) Find measure of arc ED
ii) Measure of arc COB
iii) Measure of AB
iv) Measure of arc BOE.
Solution :
i) measure of ED :
m ED = 90˚ - 15˚
m ED = 75˚
ii) m∠COB :
m∠COB = 360˚ - 90˚ - 75˚ - 15˚ - 15˚
= 360˚ - 195˚
m∠COB = 165˚
iii) m AB :
m AB = 360˚ - (90˚ + 75˚ + 15˚ + 165˚)
= 360˚ - 345˚
m AB = 15˚
iv) m∠BOE :
m∠BOE = 90˚ + 15˚
m∠BOE = 105˚
Problem 7 :
i) Measure of arc AE
ii) Measure of AB
iii) Measure of arc ECB
iv) Measure of arc BOC
Solution :
measure of arc AE :
m AE = 180˚ - 60˚ - 50˚
m AE = 70˚
measure of arc AB :
m AB = 180˚ - 60˚ - 70˚
m AB = 50˚
measure of arc ECB :
m ECB = 360˚ - m EAB
= 360˚ - (m AE + m AB)
= 360˚ - (70˚ + 50˚)
m ECB = 240˚
measure of arc ∠BOC :
m∠BOC = 180˚ - ∠DOC
= 180˚ - 50˚
m∠BOC = 130˚
Problem 8 :
i) Find measure of arc DC.
ii) Measure of EAB
iii) Measure of ACB
iv) Measure of AOB.
Solution :
measure of arc DC :
m DC = m∠COB
= 110˚ - 50˚
m DC = 60˚
measure of arc EAB :
m EAB = 180˚ - 110˚
m EAB = 70˚
m ACB :
m ACB = 180˚ + 110˚
m ACB = 290˚
m∠AOB :
m∠AOB = 180˚ - 110˚
m∠AOB = 70˚
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