All categories

3 years ago

∠ABC is adjacent to ∠CBD. If the m∠ABC=4x+23, m∠CBD=6x+7, and m∠ABD=130°, what is the measure of angle ABC? (Show your work)

Mathematics

1 answer:

Hunter-Best [27]3 years ago

7 0

Answer:

$\angle ABC=63\textdegree$

Step-by-step explanation:

$\angle ABC=4x+23\\\angle CBD=6x+7\\\angle ABD=130\textdegree \\\angle ABD=\angle ABC+\angle CBD\\\\\Rightarrow4x+23+6x+7=130\\\Rightarrow10x+30=130\\\Rightarrow10x=100\\\Rightarrow x=10$

Substitute the value of $x$

$\angle ABC=4x+23\\=4\times10+23\\=40+23\\=63$

You might be interested in

Suppose $7,558.20 in interest was earned after $12,350 was invested at a simple interest rate of 7.65%. How long (in years) was

vladimir1956 [14]

The formula is
I=prt
I interest earned 7558.20
P principle 12350
R interest rate 0.0765
T time?
Solve the formula for t by dividing both sides by pr to get
T=I/pr
T=7,558.20÷(12,350×0.0765)
T=8 years

Hope it helps!

5 0

3 years ago

Can someone please help me out here? The grading system where I’m from is a,b,c,d,and f . But for some reason I have all L’s on

Sergeu [11.5K]

Answer: just call your daddy i will

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

If -6x + 1 = -11 then x = -2<br> true or false

leva [86]

Answer:

False

Step-by-step explanation:

p(×)= -6x+1=-11

p(-2)= -6×-2+1=11

LHS=13

RHS=11

LHS≠RHS

Answer: false

5 0

2 years ago

In triangle ABC, a = 7, b = 3, and cos C=. The value of c is

mihalych1998 [28]

Answer: 7.615

Step-by-step explanation:

6 0

4 years ago

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.

saveliy_v [14]

Answer: Choice B

12.5 < x < 18.9

================================================

Explanation:

We have a triangle with these side lengths:

a = 10
b = 16
c = x = unknown

Let's assume that b = 16 is the largest side of this triangle.

By the converse of the pythagorean theorem, we need $b^2 < a^2+c^2$ to be true in order for an acute triangle to happen.

So,

$b^2 < a^2 + c^2\\\\c^2 > b^2 - a^2\\\\c > \sqrt{b^2-a^2}\\\\x > \sqrt{16^2-10^2}\\\\x > \sqrt{156}\\\\x > 12.4899959967968 \ \text{(approximate)}\\\\x > 12.5$

Now let's consider the possibility that the missing side x is actually the longest side.

Using the same theorem as before, we would say,

$c^2 < a^2 + b^2\\\\c < \sqrt{a^2 + b^2}\\\\x < \sqrt{10^2 + 16^2}\\\\x < \sqrt{356}\\\\x < 18.8679622641132 \ \text{(approximate)}\\\\x < 18.9\\\\$

We found that x > 12.5 and x < 18.9

This is the same as saying 12.5 < x and x < 18.9

Put together, they form the approximate answer of 12.5 < x < 18.9

6 0

3 years ago