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Answer :
Final answer:
To find the value of x, use the fact that AC bisects angle BAD and set up an equation: 2x - 5 = 145. Solving for x, we get x = 75. Therefore, the correct answer is option a. 75.
Explanation:
To find the value of x in the given problem, we can use the fact that AC bisects angle BAD. Since AC bisects the angle, the measure of angle BAC is equal to the measure of angle CAD.
We are given that the measure of angle BAC is 2x - 5.
Therefore, we can set up an equation: 2x - 5 = 145.
Solving for x, we get x = 75. Therefore, the correct answer is option a. 75.
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Rewritten by : Barada
∠BAD is bisected by AC . If m∠BAC= 2x - 5 and m∠CAD = 145, the value of x is a. 75.
To solve this problem, we need to determine the value of x given the information about the angles in the problem. The problem states that ∠BAD is bisected by AC and provides the measures for ∠BAC and ∠CAD as follows:
- m∠BAC = 2x - 5
- m∠CAD = 145°
Since AC bisects ∠BAD, we know that ∠BAC and ∠CAD are two equal parts of ∠BAD. Specifically, this tells us that m∠BAD = 2 * m∠BAC because ∠BAC and ∠CAD are the same angle (since AC bisects ∠BAD).
We are given that m∠CAD = 145°. Therefore, m∠BAC = m∠CAD = 145°. Since m∠BAC is given as 2x - 5, we set up the following equation:
2x - 5 = 145
Now, we solve for x:
Add 5 to both sides:
2x - 5 + 5 = 145 + 5
2x = 150Divide both sides by 2:
2x / 2 = 150 / 2
x = 75
