Question

please please please answer me this is my school holidays homework please answer me tomorrow submit madk please please answer me fast ​

Answer 1

Answer:

12)In the given triangle, ∆ABC, AB, BC, and CA represent three sides. A, B and C are the three vertices and ∠ABC, ∠BCA and ∠CAB are three interior angles of ∆ABC.

Angle Sum Property of a Triangle

Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Proof:

Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line PQ←→ parallel to the side BC of the given triangle.

Since PQ is a straight line, it can be concluded that:

∠PAB + ∠BAC + ∠QAC = 180°  ………(1)

SincePQ||BC and AB, AC are transversals,

Therefore, ∠QAC = ∠ACB (a pair of alternate angle)

Also, ∠PAB = ∠CBA (a pair of alternate angle)

Substituting the value of ∠QAC and∠PAB in equation (1),

∠ACB + ∠BAC + ∠CBA= 180°

Thus, the sum of the interior angles of a triangle is 180°

13)∠A=55,∠B=40,∠C=?

    ∠A+∠B+∠C=180

     55+40+∠C=180

     95+∠C=180

     ∠C=180-95=85

14)Let x stand for the measure of angle 1. Then. 2x for angle 2 and finally 3 x                for angle 3.  

    So, x + 2x + 3x = 180

    and 6x = 180  

     Therefore, x = 30, 2x = 60 and 3x = 90.

15)a)2+(3+4)=(2+3)+4

       9=9=associative property

    b)2*8=8*2

       16=16=associative property.

16)5/6+11/13

  =(65+66)/78

  =131/78

  =1.67

17)2/11*33/14

 =66/154

 =0.428

18)14 - 2 × 60 ÷ 15

   =14-2*4

   =14-8

   =6

19)a)x+3=11

      x=11-3=8

    b)5x=3x+2

       5x-3x=2

       2x=2

       x=1

Step-by step explanation

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