Question

1. State whether triangles are possible with the following angles:
(i) 50°, 70° and 80° (ii) 48°, 62° and 70° (iii) 67°, 53° and 60°
2. Two angles of a triangle are of measures 40° and 60° respectively. Find the
measure of the third angle.
3. In AABC, ZA = 70° and ZB = ZC . Find ZB.
4. The three angles of a triangle are equal in measures. Find the measure of each
angle.
​

Answer 1

Answer:

1. (i) Not possible (ii) Possible (iii) Possible

2. 80°

3. 55°

4. 60°

Step-by-step explanation:

The sum of all the angles of a triangle is always 180°

Answer 2

Answer:

1) -(i) triangle is not possible , (ii) triangle is possible (ii) triangle is possible

    2)80 ° is the required  measure of the third angle

   3)angle ∠B is 55°  and 4) the measure of each angle is 60° .

Step-by-step explanation:

Explanation:

As we know that sum of angle of triangle is 180 °.

Step 1:

i) 50 °, 70 °and 80 °

⇒ 50+ 70 + 180 = 200 °≠ 180 °

Triangle is  not possible

ii) 48° , 62° and 70 °

⇒ 48 + 62 + 70 = 180  , triangle is possible .

iii)67°, 53° and 60 °

⇒ 67 + 53 + 60 = 180  , triangle is possible .

Step 2:

Given , two angle of triangle are 40° and 60 °.

Let the third angle be x .

∴ 40 + 60 + x = 180           [sum of angle of triangle is 180 °]

⇒ x = 180 - 100 = 80 °

Step 3:

Given , Δ ABC in which ∠ A = 70° and ∠B = ∠C

∴∠ A + ∠B + ∠C = 180       [Sum of angle of triangle is 180]

⇒70 + 2∠B = 180         [ Given , ∠ A = 70° and ∠B = ∠C]

⇒2∠B = 180 - 70 = 110

⇒∠B = $\frac{110}{2}$ = 55°

Step 4:

Given , three angles of triangle are equal in measure .

Let  the angles be x .

Therefore ,

∠x+∠x+∠x = 180       [Sum of angle of triangle is 180°]

⇒3∠x = 180 ⇒∠x  = 60 °

Final answer:

Hence , 1) -(i) triangle is not possible , (ii) triangle is possible (ii) triangle is possible .

              2)80 ° is the measure of the third angle

              3)angle ∠B is 55°  and 4)60° is the measure of each angle .

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