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Calculate the size of angle ABC in each of these triangles. X B b A a 570 A 95⁰ 55⁰ 60% 5 Calculate the size of angle BCD in each of these diagrams. B b A C 110⁰ C 49⁰ 63° C 9⁰ D A B B 125% 30° 40° 62⁰ 289 b C 6 Three angles of a quadrilateral are 60°, 80° and 110°. How big is the fourth angle? 7 Calculate the sizes of the lettered angles in these quadrilaterals. 35° D 25 C Q 35° 71% D B 172 38° B 132 100⁰ A​

Calculate the size of angle ABC in each of these triangles X B b A a 570 A 95 55 60 5 Calculate the size of angle BCD in each of these diagrams B b A C 110 C 49 class=

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Answer:

4.

∠ABC + ∠BCA + ∠CAB = 180

therefore, ∠ABC = 180 - ∠BCA - ∠CAB

using this formula to solve 4a, 4b and 4c:

4a. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 49 -57 = 26

∠ABC = 26

4b. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 28 -90 = 62

∠ABC = 62

4c. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 38 - 25 = 117

∠ABC = 117

5a. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180

∠BCA = 180 - ∠CAB - ∠ABC = 180 - 55 - 60 = 65

∠BCA = 65

∠BCD + ∠BCA = 180

therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 65 = 115

∠BCD =115

5b. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180

∠BCA = 180 - ∠CAB - ∠ABC = 180 - 125 - 30 = 25

∠BCA = 25

∠BCD + ∠BCA = 180

therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 25 = 155

∠BCD = 155

5c. ∠ABD + ∠CBD = 180

therefore ∠CBD = 180 - ∠ABD = 180 - 132 = 48

∠CBD = 48

In the Triangle BCD, ∠CBD + ∠BDC + ∠BCD = 180

therefore ∠BCD = 180 - ∠CBD - ∠BDC = 180 - 48 - 71 = 61

∠BCD =61

6. 4 angles of a quadrilateral = 360

∠a+110+60+80=360

∠a=360-110-60-80=110

∠a = 110

7. four angles of a quadrilateral = 360

using his formula to solve for ∠a, ∠b and ∠c.

for angle a: ∠a+110+95+63=360

∠a=360-110-95-63=92

∠a = 92

for angle b: ∠b+40+62+35=360

∠b=360-40-62-35=223

∠b=223

for angle c: ∠c+100+172+35=360

∠c=360-100-172-35=53

∠c=53

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