Question

calculate the size of all angles marked with variables in the following diagrams. give reasons

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

a. ∠a=112° ( interior alternate angles are equal )

∠a=∠b ( vertically opposite angles)

∠b=112°

b. 45°+105°+y=180°(angle sum property of a triangle)

y = 180°-150°

∠y=30°

∠z=45° (interior alternate angles are equal)

x+y+z=180° (Linear Pair)

x+30+45=180

x=180-75

∠x=105°

c. ∠c=40° (Vertically opposite angles)

∠e=∠c (interior alternate angles)

∠e=40°

∠e+∠d+72=180°(angle sum property of a triangle)

∠d+40°+72°=180°

∠d=180°-112°

∠d=62°

∠d=∠a(vertically opposite angles)

∠a=62°

∠a+∠b+40°=180°(Linear pair)

60°+∠b+40°=180°

∠b=180°-100°

∠b=80°

d. ∠a=39°(interior alternate angle)

∠b+39°+39°=180°(angle sum property of a triangle)

∠b=180°-108°

∠b=72°

e.∠x+110=180°(Linear pair)

∠x=80°

∠x=∠y(corresponding angles)

∠y=80°

∠y+∠z=180°(angles on the same side of transversal)

∠z=180°-80°

∠z=100°

f.∠y=60°(interior alternate angles)

∠x=45°(interior alternate angles)

g.∠y=60°(corresponding angles)

∠z+98=180°(Linear pair)

∠z=180-98

∠z=82°

∠x=∠z(corresponding angles)

∠x=82°

h.∠x=42°(interior alternate angles)

∠z=65°(interior alternate angles)

∠x+∠y=180(Linear pair)

42°+∠y=180°

∠y=138°

i.∠a=40°(interior alternate angles)

∠a+∠b=180°(linear pair)

∠b=180°-40°

∠b=140°

∠d+105°=180°(linear pair)

∠d=180°-105°

∠d=75°

∠c=∠d(corresponding angles)

∠c=75°

∠e=105°(corresponding angles)

• Interior alternate angles are formed when a transversal intersects two coplanar lines.
• Corresponding angles are formed on the same side of one or two lines cut by a transversal.
• Vertically opposite angles are opposite angles formed by intersecting lines.

Learn more about angle sum property and vertically opposite angles by clicking on the links given below-

https://brainly.in/question/149661?referrer=searchResults

https://brainly.in/question/1146757?referrer=searchResults