Let's go through each problem based on the image provided and solve for the missing angles.

a)

• Given that one angle is 58°, and the lines appear to be parallel, the angle $a$ is its corresponding angle. $a = 58°$

b)

• This setup shows vertically opposite angles, meaning that $b$ will be equal to the given 56°. $b = 56°$

c)

• The problem involves two parallel lines and a transversal. $c$ is the alternate interior angle corresponding to 65°. $c = 65°$

d)

• The two lines intersect and the angle $d$ is vertically opposite the given 61°, so they are equal. $d = 61°$

e)

• The given angle is 68°, and $e$ is a supplementary angle (forms a linear pair with 68°). To find $e$: $e = 180° - 68° = 112°$

f)

• $f$ is the alternate interior angle to the given 49° in the parallel lines and transversal setup. $f = 49°$

g)

• $g$ and 28° are alternate interior angles. Therefore: $g = 28°$

h)

• Here, the angles form a linear pair. The sum of $h$ and 140° should equal 180°: $h = 180° - 140° = 40°$

i)

• The given angle is 62°, and $i$ is a supplementary angle (a linear pair) with 62°: $i = 180° - 62° = 118°$

j)

• The given angles are 70° and 300°, and we know a full circle is 360°, so we subtract: $j = 360° - 300° = 60°$

Here’s the summary of all solutions:

• $a = 58°$
• $b = 56°$
• $c = 65°$
• $d = 61°$
• $e = 112°$
• $f = 49°$
• $g = 28°$
• $h = 40°$
• $i = 118°$
• $j = 60°$

Would you like further details on any of these answers or explanations?

Related Questions:

1. What are alternate interior angles, and why are they equal?
2. How do vertically opposite angles relate to one another?
3. Can you explain how supplementary angles work with examples?
4. How do corresponding angles function in parallel line setups?
5. How do you identify linear pairs in geometric diagrams?

Tip:

When dealing with parallel lines and transversals, look for alternate interior, corresponding, or vertically opposite angles as they often provide quick solutions.