Question

please solve 8 and 9 ​

Answer 1

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8) GiveN:

• There are two complementary angles.
• One is 10° less than 3 times the other.

To FinD:

• The measure of these angles?

Step-by-Step Explanation:

Let one of the angles be x.

Then other angle will be 3x - 10°

Complementary angles add upto 90°.

⇒ 3x - 10° + x = 90°

⇒ 4x - 10° = 90°

⇒ 4x = 100°

⇒ x = 100° / 4

⇒ x = 25°

Then, 3x - 10° = 65°

The required angles are 25° and 65° (Answer)

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9) As the two lines intersect each other at O, the vertically opposite angles will be equal in measure. Then,

⇒ Angle DOB = Angle AOC

⇒ 2a - 5° = a + 35°

⇒ 2a - a = 35° + 5°

⇒ a = 40°

Now taking DC straight line. Angle DOA and Angle AOC will add upto 180° because they are in the same staright line.

⇒ Angle AOD + Angle AOC = 180°

⇒ b + a + 35° = 180°

⇒ b + 75° = 180°

⇒ b = 105°

Angle b and Angle c are vertically opposite angles. So, they are equal in measure.

The required values of the angles are:

• a = 40°
• b = 105°
• c = 105°

Answer 2

Answer:

Question 8

Given

• First complementary angle = 10⁰ less than the other

SoluTion

• Let the first angle be y
• second angle = 3y - 10

3y - 10 + y = 90

4y - 10 = 90

4y = 90 + 10

4y = 100⁰

y = 100/4

y = 25⁰

Then the second angle = 3y - 10 =65⁰

Verification

$y + 3y - 10 = 90$

$25 + (3 \times 25 - 10) = 90$

$25 + (75 - 10) = 90$

$25 + 65 = 90$

$90 = 90$

LHS = RHS

Question 9

The two lines are interesting each other at O . Then the measure of vertically opposite angle will be equal.

Angle AOD = Angle AOC = 180⁰

b + a + 35 = 180⁰

b + 75⁰ = 180⁰

b = 180⁰ - 75⁰

b = 105⁰

Angle B and C are vertically opposite angle. So they will equal.

• A = 45⁰
• B = 105⁰
• C = 105⁰