Question

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Answer 1

Answer:

12.) 2) x=50°

13.) 4) 119° , 119°

Step-by-step explanation:

✧ Given:-

(i) The angles on the line are (x+20)° , (x+3)° and (x+7)°.

(ii) ∠1=∠2 and ∴ ∠3=∠4 and an unequal angle in the triangle is 58°.

✧ To Find:-

(i) The Value of x.

(ii) Measure of ∠3 and ∠4.

✧ We Know That:-

• Sum of all the angles on a line is 180°.
• Sum of all angles of a triangle is 180°.

✧ Solution:-

(i) According to the Question:-

⇒ (x+20)+(x+3)+(x+7)=180

⇒ 3x+30=180

⇒ 3(x+10)=180

⇒ x+10=60

⇒ x=60-10

→ x=50°

(ii) In Δ,

   58+∠1+∠2=180

⇒ 50+∠2+∠2=180

⇒ 2∠2=180-58

⇒ ∠2=$\frac{122}{2}$

⇒ ∠2=61°

∴ ∠1=∠2=61°

Now,

 ∠3+∠1=180°

⇒ ∠3+61°=180°

⇒ ∠3=180°-61°

⇒ ∠3=119°

→ ∠3=∠4=119°