196k views
15 votes
Please help me with this problem!!

Please help me with this problem!!-example-1
User SOF User
by
7.9k points

1 Answer

5 votes

Answer:

m∠3 = 33°

Explanation:

Given that ∠1, ∠2, and ∠3 are adjacent angles, and that ∠1 and ∠2 are supplementary, while ∠2 and ∠3 are complementary angles.

We are also given the values for the following angles:

m∠1 = (8x + 3)°

m∠2 = (5x - 18)°

In order to find the measure of ∠3, we must first find the value of x using the details from the given prompt.

We know that ∠1 and ∠2 are supplements, which means that the sum of their measures add up to 180°. In other words:

m∠1 + m∠2 = 180°

Substitute the given values into the equation:

(8x + 3)° + (5x - 18)° = 180°

8x° + 3° + 5x° - 18° = 180°

Combine like terms:

13x° - 15° = 180°

Add 15° from both sides:

13x° - 15° + 15° = 180° + 15°

13x° = 195°

Divide both sides by 13 to solve for x:


\displaystyle\mathsf{(13x^(\circ))/(13^(\circ))\:=\:(195^(\circ))/(13^(\circ)) }

x = 15°

Now that we have the value for x = 15°, we need to determine the measure of ∠3. Using the details from the given prompt that m∠2 and m∠3 are complementary angles (whose measures add up to 90°), then we can set up the following equation:

m∠2 + m∠3 = 90°

Substitute its value into m∠2° to find the m∠3°.

m∠2 + m∠3 = 90°

(5x - 18)° + m∠3 = 90°

5(15)° - 18° + m∠3 = 90°

75° - 18° + m∠3 = 90°

57° + m∠3 = 90°

Subtract 57° from both sides:

57° - 57° + m∠3 = 90° - 57°

m∠3 = 33°

Therefore, the measure of ∠3 is 33°.

Double-check:

In order to verify whether we have the correct measure for ∠3, we'll substitute the x = 15° into the given values for ∠1, ∠2, and the derived value for ∠3.

m∠1 + m∠2 = 180°

(8x + 3)° + (5x - 18)° = 180°

8(15)° + 3° + 5(15)° - 18° = 180°

120° + 3° + 75° - 18° = 180°

180° = 180° (True statement).

m∠2 + m∠3 = 90°

(5x - 18)° + 33° = 90°

5(15)° - 18° + 33° = 90°

75° - 18° + 33° = 90°

90° = 90° (True statement).

User Robert Franke
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories