(1) ∠ABC = 65°, ∠DBE = 65°, ∠CBE = 115°, ∠ABD = 115°
(2) ∠ABC = 62°, ∠DBE = 62°, ∠CBE = 118°, ∠ABD = 118°
Solution:
(1) In the given image ABC and DBE are vertical angles.
<u>Vertical angle theorem:</u>
If two angles are vertical then they are congruent.
⇒ ∠ABC = ∠DBE
⇒ 3x° + 38° = 5x° + 20°
Arrange like terms one side.
⇒ 38° – 20° = 5x° – 3x°
⇒ 18° = 2x°
⇒ x° = 9°
∠ABC = 3(9°) + 38° = 65°
∠DBE = 5(9°) + 20° = 65°
Adjacent angles in a straight line = 180°
⇒ ∠ABC + ∠CBE = 180°
⇒ 65° + ∠CBE = 180°
⇒ ∠CBE = 115°
∠ABD and ∠CBE are vertical angles.
∠ABD = 115°
(2) In the given image ABC and DBE are vertical angles.
⇒ ∠ABC = ∠DBE
⇒ 4x° + 2° = 5x° – 13°
Arrange like terms one side.
⇒ 13° + 2° = 5x° – 4x°
⇒ 15° = x°
∠ABC = (4(15°) + 2°) = 62°
∠DBE = 5(15°) – 13° = 62°
Adjacent angles in a straight line = 180°
⇒ ∠ABC + ∠CBE = 180°
⇒ 62° + ∠CBE = 180°
⇒ ∠CBE = 118°
∠ABD and ∠CBE are vertical angles.
∠ABD = 118°
Answer 3,5,7
Step-by-step explanation:
Answer:
513
Step-by-step explanation:
B×L=Area
Base=24
Length =19
24×19=513
Answer:
√41
Step-by-step explanation:
Use the distance formula.
(3, 1) and (-2,-3)
The distance between 3 and -2 is 5. 5 squared is 25.
The distance between 1 and -3 is 4. 4 squared is 16.
25+16 = 41
the root of 41 is √41.
