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In this lesson, we will learn how to identify vertically opposite angles.

Q1:

If two angles are vertically opposite, are they equal in measure?

Q2:

Given that lines ⃖ ⃗ 𝐴 𝐵 and ⃖ ⃗ 𝐶 𝐷 intersect at 𝑂 , find 𝑚 ∠ 𝐴 𝑂 𝐶 .

Q3:

In the figure, lines ⃖ ⃗ 𝐴 𝐵 and ⃖ ⃗ 𝐶 𝐷 intersect at 𝐿 . What is 𝑚 ∠ 𝐴 𝐿 𝐷 ?

Q4:

Find the value of 𝑥 .

Q5:

In the given diagram, 𝑚 ∠ 𝐴 𝑋 𝐵 = ( 4 𝑥 − 8 ) ∘ and 𝑚 ∠ 𝐶 𝑋 𝐷 = 4 4 ∘ . Find the value of 𝑥 .

Q6:

Knowing that ⃖ ⃗ 𝐴 𝐵 ∩ ⃖ ⃗ 𝐶 𝐷 ∩ ⃖ ⃗ 𝑂 𝐸 = { 𝑀 } , 𝑚 ∠ 𝐸 𝑀 𝐷 = 6 1 ∘ , 𝑚 ∠ 𝐶 𝑀 𝐵 = 6 7 ∘ , and 𝑚 ∠ 𝑂 𝑀 𝐴 = 𝑥 , find 𝑥 .

Q7:

Two intersecting straight lines are shown. Find the values of 𝑥 and 𝑦 .

Q8:

If ∠ 𝑎 and ∠ 𝑏 are vertical angles, where 𝑚 ∠ 𝑎 = ( 2 𝑥 − 1 0 ) ∘ and 𝑚 ∠ 𝑏 = ( 𝑥 + 7 ) ∘ , find 𝑚 ∠ 𝑎 and 𝑚 ∠ 𝑏 .

Q9:

In the figure, , , , and . Find the values of and .

Q10:

In the given diagram, 𝑚 ∠ 𝐴 𝑋 𝐵 = 4 0 ∘ . Find 𝑚 ∠ 𝐶 𝑋 𝐷 .

Q11:

Calculate 𝑚 ∠ 𝐶 𝑀 𝐹 .

Q12:

What is in the following figure?

Q13:

Q14:

Find the value of 𝑥 in the given diagram.

Q15:

Lines 𝐴 𝐶 and 𝐵 𝐷 meet at 𝑂 . Determine the value of 𝑥 .

Q16:

In the figure rays 𝐴 𝐸 and 𝐶 𝐷 meet at 𝐵 , and 𝑚 ∠ 𝐷 𝐵 𝐸 = 5 9 ∘ . What is 𝑚 ∠ 𝐵 𝐴 𝐶 ?

Q17:

In the given figure, if 𝑚 ∠ 𝑋 𝐵 𝐸 = 3 6 ∘ and 𝑚 ∠ 𝑍 𝐴 𝑌 = 1 0 1 ∘ , find 𝑚 ∠ 𝐹 𝐶 𝐵 .

Q18:

Which of the following statements is always true of vertically opposite angles?

Q19:

What is the sum of the measures of the two adjacent angles formed by a straight line and a ray?

Q20:

Which of these is the supplement of an acute angle?

Q21:

If 𝑚 ∠ 𝐴 + 𝑚 ∠ 𝐵 = 1 8 0 ∘ , then ∠ 𝐴 and ∠ 𝐵 are .

Q22:

Two angles are supplementary and one of them is a . What is the other?

Q23:

In the given diagram, ∠ 𝐴 𝐵 𝐶 is a right angle and 𝑚 ∠ 𝐴 𝐵 𝐷 = 6 3 ∘ . Work out 𝑚 ∠ 𝐷 𝐵 𝐶 .

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