All categories

2 years ago

According to the figure given here,

Mathematics

2 answers:

AfilCa [17]2 years ago

4 0

Answer:

(i) 90°

(ii) CÔD

(iii) AÔD = 110°

(iv) 180°

(v) AÔD

(vi) AÔB

Step-by-step explanation:

Two angles are said to be complementary if they add up to 90°.

Complementary angles can either be adjacent or non-adjacent.

Two Angles are said to be supplementary if they add up to 180°.

Complementary angles can either be adjacent or non-adjacent.

(i) BÔC + CÔD = 25 + 65 = 90°

(ii) BÔC = 25°

Therefore the complementary angle measures 90 - 25 = 65°

So the complement of BÔC is CÔD

(iii) AÔD = 20 + 25 + 65 = 110°

(iv) AÔD + DÔE = 110 + 70 = 180°

(v) DÔE = 70°

Therefore the supplementary angle measures 180 - 70 = 110°

So the supplement of DÔE is AÔD

(vi) DÔE = 70°

Therefore the complementary angle measures 90 - 70 = 20°

So the complement of DÔE is AÔB

Readme [11.4K]2 years ago

4 0

<BOC+<COD=25+65=90

Let the complement be x

x=90-25=75

<AOD=20+25+65=110

<AoD+<DOE=110+70=180°

x=90-70=20

You might be interested in

Help me please ASAP!!!!

gogolik [260]

It took 8 weeks because follow 15 to the dot then go down and you see the answer

3 0

4 years ago

Read 2 more answers

Question 7 Essay Worth 5 points)

TEA [102]

Answer:This is a tricky question that Reina and Sam are multiplying (84)5 (73)9 and their work are (84)5 (73)9 = 84 + 573 + 9 = 89712 Reina's (84)5 (73)9 = 84-573-9 = 820727 Sam's Actually they are doing or multiplying using exponents. Reina's work (8*)s(7³)º=8*+5+ 73+9= 8° 712 This is incorrect because she added exponents instead of multiplying exponents Sams work (8*)5 (7³)º=84x5 73x9= 820 727 This is correct because Sam multiplied exponents correctly Exponents are multiplied not added.

7 0

3 years ago

What is $34.00 with 25% off

Furkat [3]

34 * .25 = 8.5

34 - 8.5 = 25.5

It's $25.5 with 25% off.

5 0

3 years ago

Read 2 more answers

Paula bought a ski jacket on sale for $7 less than half its original price. She paid $84 for the jacket. What was the original p

Eddi Din [679]

1/2x - 7 = 84
1/2x = 84 + 7
1/2x = 91
x = 91 / (1/2)
x = 91 * 2
x = 182 <=== original price

5 0

3 years ago

In the trapezoid ABCD (AB∥CD) point M∈AD, so that AM:MD=3:5. Line L ∥AB and going through point M intersects diagonal AC and leg

siniylev [52]

Answer:

$\dfrac{AP}{PC}=\dfrac{3}{5}$

$\dfrac{BN}{CN}=\dfrac{3}{5}$

Step-by-step explanation:

Consider triangles AMP and ADC. In these triangles,

angle A is the common angle, so $\angle MAP\cong \angle DAC$ by reflexive property;
angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.

Hence, triangles AMP and ADC are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

$\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,$

$\dfrac{AP}{PC}=\dfrac{\frac{3}{8}AC}{\frac{5}{8}AC}=\dfrac{3}{5}$

Consider triangles ACB and PCN. In these triangles,

angle C is the common angle, so $\angle ACB\cong \angle PCN$ by reflexive property;
angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.

Hence, triangles ACB and PCN are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

$\dfrac{CP}{AP}=\dfrac{CN}{CB}\\ \\\dfrac{5x}{3x+5x}=\dfrac{CN}{CB}\\ \\\dfrac{CN}{CB}=\dfrac{5}{8}\Rightarrow CN=\dfrac{5}{8}CB\\ \\BN=BC-CN=BC-\dfrac{5}{8}BC=\dfrac{3}{8}BC,$

$\dfrac{BN}{CN}=\dfrac{\frac{3}{8}BC}{\frac{5}{8}BC}=\dfrac{3}{5}$

4 0

3 years ago