Question

UN 51
6. Use the properties of triangles to find the unknown angles.
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Answer 1

Answer:

Figure C: x = 45°

Step-by-step explanation:

65°+ 70°+x=180°

Answer 2

Answer:

Step-by-step explanation:

Solutions :-

Figure -1:-

In ∆ ABC , angle CAB = 65°

AB = AC => angle ACB = angle CBA

Since the angles opposite to equal sides are equal.

Let angle ACB = angle CBA = A°

We know that

The sum of all angles in a triangle is 180°

=> angle ACB + angle CBA + angle CAB = 180°

=> A°+A°+65° = 180°

=> 2A°+65° = 180°

=> 2A° = 180°-65°

=> 2A° = 115°

=> A° = 115°/2

=> A° = 57.5°

angle ACB = angle CBA = 57.5°

and

In ∆ BCD , angle BCD = 110°

and

BC = CD => angle BDC = angle CBD

Since the angles opposite to equal sides are equal.

Let angle BDC = angle CBD = M°

The sum of all angles in a triangle is 180°

angle BCD+angle BDC + angle CBD = 180°

=> M°+M°+110° = 180°

=> 2M°+110°° = 180°

=> 2M° = 180°-110°

=> 2M° = 70°

=> M° = 70°/2

=> M° = 35°

Therefore, angle BDC = angle CBD = 35°

Now,

angle B = angle ABC+ angle CBD

=> x = 57.5°+35°

=> x = 92.5°

therefore, x = 92.5°

Answer:-

Figure -1:-

x = 10° and y = 105°

Figure -2:-

x = 92.5°

Used formulae:-

1. The sum of all angles in a triangle is 180°

2. the angles opposite to equal sides are equal.

3. The exterior angle of a triangle formed by extending one side is equal                   to the sum of the opposite interior angles.  

THIS IS THE SOLUTION

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