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2 years ago

Find the measures of the interior angles.

Mathematics

1 answer:

NARA [144]2 years ago

6 0

Answer:

angle A: 59 degrees

angle B: 48 degrees

angle C: 73 degrees

Step-by-step explanation:

in every triangle, if you add up all of the degrees, you get 180

x + 73 + (x - 11) = 180

2x + 62 = 180

2x = 118

x = 59

then, you can just insert x into the respected expressions to solve for their angles

A. x = 59 degrees

B. x - 11

59 - 11

48 degrees

C. 73 degrees

You might be interested in

If each quadrilateral below is a parallelogram,find the missing measures.

zhenek [66]

Answer:

Part 1) $MN=31\ units$

Part 2) $KN=45\ units$

Part 3) m∠K=61°

Part 4) m∠L=119°

Part 5) m∠M=61°

Step-by-step explanation:

we know that

In a parallelogram opposite angles and opposite sides are congruent and consecutive angles are supplementary

Part 1) Find the side MN

we know that

MN≅KL ----> by opposite sides

we have

$KL=31\ units$

therefore

$MN=31\ units$

Part 2) Find the side KN

we know that

KN≅LM ----> by opposite sides

we have

$LM=45\ units$

therefore

$KN=45\ units$

Part 3) Find the measure of angle K

we know that

m∠K+m∠N=180° ----> by consecutive interior angles

we have

m∠N=119°

substitute

m∠K+119°=180°

m∠K=180°-119°

m∠K=61°

Part 4) Find the measure of angle L

we know that

m∠L≅m∠N ----> by opposite angles

we have

m∠N=119°

therefore

m∠L=119°

Part 5) Find the measure of angle M

we know that

m∠M≅m∠K ----> by opposite angles

we have

m∠K=61°

therefore

m∠M=61°

7 0

2 years ago

Solve the triangle A = 2 B = 9 C =8

VARVARA [1.3K]

Answer:

$\begin{gathered} A=\text{ 12}\degree \\ B=\text{ 114}\degree \\ C=54\degree \end{gathered}$

Step-by-step explanation:

To calculate the angles of the given triangle, we can use the law of cosines:

$\begin{gathered} \cos (C)=\frac{a^2+b^2-c^2}{2ab} \\ \cos (A)=\frac{b^2+c^2-a^2}{2bc} \\ \cos (B)=\frac{c^2+a^2-b^2}{2ca} \end{gathered}$

Then, given the sides a=2, b=9, and c=8.

$\begin{gathered} \cos (A)=\frac{9^2+8^2-2^2}{2\cdot9\cdot8} \\ \cos (A)=\frac{141}{144} \\ A=\cos ^{-1}(\frac{141}{144}) \\ A=11.7 \\ \text{ Rounding to the nearest degree:} \\ A=12º \end{gathered}$

For B:

$\begin{gathered} \cos (B)=\frac{8^2+2^2-9^2}{2\cdot8\cdot2} \\ \cos (B)=\frac{13}{32} \\ B=\cos ^{-1}(\frac{13}{32}) \\ B=113.9\degree \\ \text{Rounding:} \\ B=114\degree \end{gathered}$ $\begin{gathered} \cos (C)=\frac{2^2+9^2-8^2}{2\cdot2\cdot9} \\ \cos (C)=\frac{21}{36} \\ C=\cos ^{-1}(\frac{21}{36}) \\ C=54.3 \\ \text{Rounding:} \\ C=\text{ 54}\degree \end{gathered}$

3 0

6 months ago

Factor this trinomial.<br> x2 + 2x-3

andre [41]

Answer:(x-1) (x+3)

Step-by-step explanation:

Hope this helps!

4 0

2 years ago

A house has increased in value by 28% since it was purchase. if the current value is $416,000, what was the value when it what w

EleoNora [17]

Answer: 300,000

Step-by-step explanation:

6 0

1 year ago

What is the equation of the line h Th ya has a y intercept of (0,-3) and passes through the point (-9,-9)

Nikolay [14]

Answer:

The line equation is given as: 3 y = 2 x - 9

Step-by-step explanation:

Here, Y intercept is at point ( 0.-3)

So, at x = 0, y = -3

or, C = -3

Also, the point on the equation line is (x,y) = (-9,-9)

Now, by <u>SLOPE INTERCEPT FORM</u> of a line equation,we get:

y = m x + C : m = slope of line ......... (1)

So, substituting the values of C and (x,y) , we get:

-9 = m (-9) + (-3)

or, -9 + 3 = - 9 m

or, m = -6/-9 = 2/3

or, m = 2/3

Now, substitute the value of m back in to the line equation (1)

$y = m x + C \implies y = (\frac{2}{3}) x - 3\\\implies 3y = 2x - 9$

Hence, the line equation is given as: 3 y = 2 x - 9.

5 0

2 years ago