(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°
-7 is the answer to this question
Answer:
290 adults and 341 children
Step-by-step explanation:
1. Combine all of the like terms so that you can simplify it, if they are not combined already.
2. Drop all of the constants and coefficients, the constant terms are all of the terms that are not attached to the variable.
3. Put the term in decreasing order of their exponents.
4. Find the power o the largest term.
5. Identify the degree of the polynomial.
6. Know that the degree of a constant is zero.
Hope this helps!
We divide the total set into several sub-sets (subgroups) that contain the exact same number of members. This way we know the number of total members by adding the number of total subsets.
