Question

What angle relationship is represented below?

Circle One: Supplementary, Complementary Vertical
Solve for x.

Answer 1

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

• 
  `\tt \\rightarrow \red{5x - 60 = x + 20}`
• 
  `\tt \\rightarrow \red{ 5x - 60 - x = 20}`
• 
  `\tt \\rightarrow \red{5x - x = 20 + 60}`
• 
  `\tt \\rightarrow \red{ 4x = 80}`
• 
  `\tt \\rightarrow \red{x =20 }`

Measure of each angle ⤵️

`\green{ \bf \: 5x - 60} \\ \green{ \bf \: 5 * 20 - 60} \\ \green{ \bf \:100 - 60 } \\ \green{ \bf \: 40 \degree}`

`\blue{ \bf \: x + 20} \\ \blue{ \bf \: 20 + 20} \\ \blue{ \bf \: 40 \degree}`

Answer 2

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

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°