Ask question

Ask question

All categories

konstantin123 [22]

3 years ago

12

In triangle ABC,if measure of angle A is seven more than four times measure of angle B and measure of angle C is eleven more tha

n measure of angle B,find the measure of angle A

1 answer:

Yuri [45]3 years ago

7 0

Answer: Angle A is 115 degrees

Step-by-step explanation:

In triangle ABC, the measure of angle A is seven more than four times measure of angle B. This means that

Angle A = 4(Angle B) + 7

The measure of angle C is eleven more than measure of angle B. This means that

Angle C = Angle B + 11.

The equations are

A = 4B + 7 - - - - - - - - 1

C = B + 11 - - - - - - - - - - 2

Recall that the sum of the angles in a triangle is 180 degrees. This means that

A + B + C = 180 degrees

Substituting equation 1 and equation 2 into A + B + C = 180, it becomes

4B + 7 + B + B + 11 = 180

6B + 18 = 180

6B = 180 - 18 = 162

B = 162/6 = 27 degrees

Substituting B = 27 into equation 1, it becomes

A = 4×27 + 7 = 108 +7

A = 115 degrees

Substituting B = 27 into equation 2, it becomes

C = 27 + 11

C = 38 degrees

Sum of the angles is 115 + 27 + 38 = 180

You might be interested in

Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and ro

Helga [31]

Answer:

Part 1) The shape is a trapezoid

Part 2) The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

Part 3) The area is $937.5\ units^2$

Step-by-step explanation:

step 1

Plot the figure to better understand the problem

we have

A(-28,2),B(-21,-22),C(27,-8),D(-4,9)

using a graphing tool

The shape is a trapezoid

see the attached figure

step 2

Find the perimeter

we know that

The perimeter of the trapezoid is equal to

$P=AB+BC+CD+AD$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

we have

A(-28,2),B(-21,-22)

substitute in the formula

$d=\sqrt{(-22-2)^{2}+(-21+28)^{2}}$

$d=\sqrt{(-24)^{2}+(7)^{2}}$

$d=\sqrt{625}$

$d_A_B=25\ units$

Find the distance BC

we have

B(-21,-22),C(27,-8)

substitute in the formula

$d=\sqrt{(-8+22)^{2}+(27+21)^{2}}$

$d=\sqrt{(14)^{2}+(48)^{2}}$

$d=\sqrt{2,500}$

$d_B_C=50\ units$

Find the distance CD

we have

C(27,-8),D(-4,9)

substitute in the formula

$d=\sqrt{(9+8)^{2}+(-4-27)^{2}}$

$d=\sqrt{(17)^{2}+(-31)^{2}}$

$d=\sqrt{1,250}$

$d_C_D=25\sqrt{2}\ units$

Find the distance AD

we have

A(-28,2),D(-4,9)

substitute in the formula

$d=\sqrt{(9-2)^{2}+(-4+28)^{2}}$

$d=\sqrt{(7)^{2}+(24)^{2}}$

$d=\sqrt{625}$

$d_A_D=25\ units$

Find the perimeter

$P=25+50+25\sqrt{2}+25$

$P=(100+25\sqrt{2})\ units$

simplify

$P=25(4+\sqrt{2})\ units$ ----> exact value

$P=135.4\ units$

therefore

The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

step 3

Find the area

The area of trapezoid is equal to

$A=\frac{1}{2}[BC+AD]AB$

substitute the given values

$A=\frac{1}{2}[50+25]25=937.5\ units^2$

4 0

3 years ago

Carlo was baking cupcakes. The recipe called for 1.5 cups of sugar to make 24 cupcakes. How many cups of sugar will he need to m

IceJOKER [234]

Answer:0.75

Step-by-step explanation:12 is half of 24

Answer should be be half of 1.5

3 0

2 years ago

How many unique ways are there to arrange the letters in the word DEN?

Tatiana [17]

2 is the correct answer I'm almost definite

5 0

3 years ago

Read 2 more answers

A line passes through the points A(n,4) and B(6,8) and is parallel to y=2x-5. What is the value of n?

Lady_Fox [76]

The slope of <em>y</em> = 2<em>x</em> - 5 is 2. Parallel lines have the same slope, so the slope of the line through the given points <em>A</em> and <em>B</em> is also 2. This means

(8 - 4) / (6 - <em>n</em>) = 2

Solve for <em>n</em> :

4 / (6 - <em>n</em>) = 2

4/2 = 6 - <em>n</em>

2 = 6 - <em>n</em>

<em>n</em> = 6 - 2

<em>n</em> = 4

4 0

3 years ago

Cant seem to solve this problem, help needed.

Georgia [21]

Answer:

c

Step-by-step explanation:

3 0

3 years ago