Answer :
Answer:
Supplementary angles in diagram:
m∠ABD and m∠ABC
m∠ABD and m∠DBE
m∠DBE and m∠CBE
m∠ABC and m∠CBE
Vertical angles in diagram:
m∠ABD and m∠CBE
m∠ABC and m∠DBE
No complementary angles
x = 20
Step-by-step explanation:
Supplementary angles: two angles whose measures add up to 180°
Complementary angles: two angles whose measures add up to 90°
Vertical angles: a pair of opposite angles formed by intersecting lines. Vertical angles are congruent.
Supplementary angles in diagram:
m∠ABD and m∠ABC
m∠ABD and m∠DBE
m∠DBE and m∠CBE
m∠ABC and m∠CBE
Vertical angles in diagram:
m∠ABD and m∠CBE
m∠ABC and m∠DBE
As m∠ABD and m∠CBE are vertical angles, this means they are congruent:
⇒ m∠ABD = m∠CBE
⇒ 5x - 60 = x + 20
⇒ 4x = 80
⇒ x = 20
Therefore,
m∠ABD = m∠CBE = 40°
m∠ABC = m∠DBE = 140°
There are no complementary angles in the diagram, as there are no two angles whose sum is 90°
What angle relationship is represented below?
- The given angles are Vertically opposite angles
- They are formed on the lines that are opposite to each other at vertex.
Solve for x
- [tex] \tt \nrightarrow \red{5x - 60 = x + 20}[/tex]
- [tex] \tt \nrightarrow \red{ 5x - 60 - x = 20}[/tex]
- [tex] \tt \nrightarrow \red{5x - x = 20 + 60}[/tex]
- [tex] \tt \nrightarrow \red{ 4x = 80}[/tex]
- [tex] \tt \nrightarrow \red{x =20 }[/tex]
Measure of each angle ⤵️
[tex] \green{ \bf \: 5x - 60} \\ \green{ \bf \: 5 \times 20 - 60} \\ \green{ \bf \:100 - 60 } \\ \green{ \bf \: 40 \degree}[/tex]
[tex] \blue{ \bf \: x + 20} \\ \blue{ \bf \: 20 + 20} \\ \blue{ \bf \: 40 \degree}[/tex]
