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2 years ago

∠a and ∠b are supplementary angles. if m ∠a =(x +6)° and m ∠b= (7x +30)°, then find the measure of ∠a.

Mathematics

1 answer:

Bezzdna [24]2 years ago

5 0

Answer:

24 Degrees

Step-by-step explanation:

Supplementary Angles are two angles with a sum of 180 degrees.

x+6+7x+30=180

8x+36=180

8x=144

18=x

Plug in 18 to angle A

18+6=24

24 degrees

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Q.2

Katen [24]

Answer:

Q2. (16,8)

Q3. $k=\frac{2}{3}$ , ratio=5:1

Q4. Ratio=2:1

Q5. Ratio=1:1

Step-by-step explanation:

Q2. Let (2a,a) be the coordinates of P.

Since P is equidistant from Q (2,-5) and R (-3, 6), we have

$|PQ|=|PR|$

This gives us:

$\sqrt{(2a-2)^2+(a+5)^2}=\sqrt{(2a+3)^2+(6-a)^2}$

$\implies (2a-2)^2+(a+5)^2=(2a+3)^2+(6-a)^2$

Expand:

$4a^2-8a+4+a^2+10a+25=4a^2+12a+9+a^2 -12a+36$

$2a=16$

$a=8$

The coordinates of P are $(16,8)$

Q.3 The equation of the line segment joining the points

A (5.-6) and B (-1,-4) is $x+3y=-13$ .

The x-coordinate of the point that divides AB in the ratio m:n is

$x=\frac{mx_2+nx_1}{m+n}$

The y-axis meets this line at $(0,-\frac{13}{3})$

We substitute $x_2=-1,x_1=5,x=0$ into this equation and solve for m and n.

$0=\frac{-m+5n}{m+n}$

$m=5n$

$\frac{m}{n}=\frac{5}{1}$

Therefore the ratio is m:n=5:1

Q.4 The equation of the line segment joining

the points (-5,-4) and (-2,3) is $-7x+3y=23$ .

The point (-3, k) must satisfy this line because it lies on it.

$-7(-3)+3k=23$ .

$\implies k=\frac{2}{3}$

We again use the equation $x=\frac{mx_2+nx_1}{m+n}$ to find the given ratio.

Substitute: $x_2=-2,x_1=-5$

$4=\frac{-2m+-5n}{m+n}$

$\implies m=2n$

$\frac{m}{n}= \frac{2}{1}$

The ratio is m:n=2:1

Q. 5 The equation of the line joining A (2,3) and B(6,-3) is $3x+2y=12$ .

We substitute (4,m) to get:

12+4m=12

4m=0

m=0

It is obvious that: (4,0) is the midpoint of A(2,3) and B(6,-3).

Hence the ratio is 1:1

5 0

2 years ago

Please help me I will give you extra points and the brain thing. (image below) 3/5

JulsSmile [24]

I think the answer is A

4 0

2 years ago

I’ve been stuck can someone explain

MariettaO [177]

Answer:

Option (3)

Step-by-step explanation:

From the figure attached,

AB and CD are two chords intersecting at O.

m∠AOD = 37°

m∠AOC + m∠AOD = 180° [Since these angles are supplementary angles]

m∠AOC = 180° - 37°

= 143°

By the theorem of intersecting chords,

Measure of angle formed is the half of the sum of measures of the arcs intercepted by the angle and vertical angle.

m∠AOC = $\frac{1}{2}(\widehat{AC}+\widehat{BD})$

143° = $\frac{1}{2}[(x+5)+(x-5)]$

143° = x

Therefore, Option (3) will be the answer.

3 0

2 years ago

Help me out ?<<<<<<<<<<<

Advocard [28]

It would be J because the radius is 6 inches and the radius is only starting from the edge to the middle not fully across it can be confusing. Hope that helped!

7 0

3 years ago

2(48)+2(8w)+2(6w)=208 please explain

babymother [125]

Answer:

w=4

Step-by-step explanation:

2(48)+2(8w)+2(6w)=208

1) Start by Distributing the value outside of the parenthesis:

96+16w+12w=208

2) Combine alike terms:

96+28w=208

3) Subtract 96 from both sides:

28w=112

4)Divide both sides by 28 to isolate w:

w=4

Let me know if you do not understand :)

4 0

2 years ago