Question

What angle relationship is represented below?

Answer 1

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°

Answer 2

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

• $\tt \nrightarrow \red{5x - 60 = x + 20}$
• $\tt \nrightarrow \red{ 5x - 60 - x = 20}$
• $\tt \nrightarrow \red{5x - x = 20 + 60}$
• $\tt \nrightarrow \red{ 4x = 80}$
• $\tt \nrightarrow \red{x =20 }$

Measure of each angle ⤵️

$\green{ \bf \: 5x - 60} \\ \green{ \bf \: 5 \times 20 - 60} \\ \green{ \bf \:100 - 60 } \\ \green{ \bf \: 40 \degree}$

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