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3 years ago

Can anybody help me solve this? You must solve for x first.

Mathematics

2 answers:

DochEvi [55]3 years ago

5 0

Answer: The measure of angle ABC is 65 degrees.

Step-by-step explanation:

2x- 15 + 2x - 15 + x + x =360

6x - 30 = 360

+ 30 + 30

6x = 390

x= 65

check: 2(65) - 15 = 115

115 + 115 + 65 + 65 = 360

gavmur [86]3 years ago

3 0

Answer:

ABC = 65

Step-by-step explanation:

The sum of the angles of a quadrilateral are 360

2x-15 + x + 2x-15 +x = 360

Combine like terms

6x -30 = 360

Add 30 to each side

6x -30 +30 = 360+30

6x= 390

Divide by 6

6x/6 = 390/6

x=65

We want angle ABC

ABC = x

ABC = 65

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Alright, lets get started.

Lets check each possible answer one by one.

We will start from option B.

BC is from small triangle and its corresponding side is DF, so its ratio will be $\frac{4}{5}$ not $\frac{5}{4}$ as given in option. Hence option B is incorrect.

For option C,

Angle a° and angle f° are not similar angles, if they were similar, then only their ratio will be 1 otherwise not 1. Hence option C is incorrect.

For option D,

Angle c° and angle f° are similar angles so, their ratio will be $\frac{c}{f} = 1$ . Hence option D is incorrect.

Now option A,

ED and AB are corresponding sides. ED is from bigger triangle and AB is from smaller triangle. Their ratio will be $\frac{ED}{AB} = \frac{5}{4}$ . Hence option A is correct answer.