To solve the problem of finding the values of the unknown angles in each figure, we will use geometric properties and relationships between angles. Let's go through each figure step by step.
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Figure 1:
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Given: \( \angle AOB = 60^\circ \), \( \angle BOC = 40^\circ \)
-
Unknown: \( \angle AOC \)
Solution:
Since \( \angle AOC \) is the sum of \( \angle AOB \) and \( \angle BOC \):
\[
\angle AOC = \angle AOB + \angle BOC = 60^\circ + 40^\circ = 100^\circ
\]
Answer for Figure 1:
\[
\boxed{100^\circ}
\]
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Figure 2:
-
Given: \( \angle PQR = 120^\circ \), \( \angle RQS = 50^\circ \)
-
Unknown: \( \angle PQS \)
Solution:
Since \( \angle PQS \) is the difference between \( \angle PQR \) and \( \angle RQS \):
\[
\angle PQS = \angle PQR - \angle RQS = 120^\circ - 50^\circ = 70^\circ
\]
Answer for Figure 2:
\[
\boxed{70^\circ}
\]
---
Figure 3:
-
Given: \( \angle XYZ = 90^\circ \), \( \angle YZW = 30^\circ \)
-
Unknown: \( \angle XZW \)
Solution:
Since \( \angle XZW \) is the sum of \( \angle XYZ \) and \( \angle YZW \):
\[
\angle XZW = \angle XYZ + \angle YZW = 90^\circ + 30^\circ = 120^\circ
\]
Answer for Figure 3:
\[
\boxed{120^\circ}
\]
---
Figure 4:
-
Given: \( \angle LMN = 110^\circ \), \( \angle NMO = 70^\circ \)
-
Unknown: \( \angle LMO \)
Solution:
Since \( \angle LMO \) is the difference between \( \angle LMN \) and \( \angle NMO \):
\[
\angle LMO = \angle LMN - \angle NMO = 110^\circ - 70^\circ = 40^\circ
\]
Answer for Figure 4:
\[
\boxed{40^\circ}
\]
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Figure 5:
-
Given: \( \angle ABC = 130^\circ \), \( \angle CBD = 80^\circ \)
-
Unknown: \( \angle ABD \)
Solution:
Since \( \angle ABD \) is the difference between \( \angle ABC \) and \( \angle CBD \):
\[
\angle ABD = \angle ABC - \angle CBD = 130^\circ - 80^\circ = 50^\circ
\]
Answer for Figure 5:
\[
\boxed{50^\circ}
\]
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Figure 6:
-
Given: \( \angle DEF = 75^\circ \), \( \angle EFG = 45^\circ \)
-
Unknown: \( \angle DFG \)
Solution:
Since \( \angle DFG \) is the sum of \( \angle DEF \) and \( \angle EFG \):
\[
\angle DFG = \angle DEF + \angle EFG = 75^\circ + 45^\circ = 120^\circ
\]
Answer for Figure 6:
\[
\boxed{120^\circ}
\]
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Final Answers:
\[
\boxed{100^\circ, 70^\circ, 120^\circ, 40^\circ, 50^\circ, 120^\circ}
\]
Parent Tip: Review the logic above to help your child master the concept of pairs of angles worksheet pdf.
