Question

Find the value(s) of the unknown(s) in each of the following kites.




please help me :(

please send step by step answer​

Answer 1

Answer:

100°+a°+a°=180°(angles in a triangle)

100°+2a°=180°

2a°=180°-100°

2a°=80°(divide both sides by coefficient of a)

a=40°

40°+26°+c°=180°(angles in a triangle)

66°+c°=180°

c°=180-66

c°=114°

Answer 2

Answer:

In (a) ∠a = 40°, ∠b = 58°

In (b) ∠c = 114°

Step-by-step explanation:

In figure (a),

DAC is a triangle and ACB is a triangle.

If we slit the kite in two halves from the middle there is intersection of DB with AC, (refer the attachment)

When we cut 100° in two equal parts, the answer results in 50°.

measure of angle E = 90

The new triangle (shown in red) DAE is formed.

Sum of the angles in triangle DAE = 180°

So, We know the measures of angles D and E, insert them,

50° + 90° + a° = 180°

50 + a = 180 - 90

50 + a = 90

a = 90 - 50

m∠a = 40

As the two angles A and C as per the properties of angles of kite are equal, then angle g = 40° and angle k = 61°

Now, we know that the sum of interior angles of any quadrilateral is 360° then to find b, lets apply that property.

Out of the four angles of the kite, three are known,

angle d= 100, angle AK = 101 and angle GC = 101 and then there's angle b

100 + 101 +101 + b = 360

302 + b = 360

b = 360 - 302

b = 58°

In figure (b),

We will be working with triangles AYB and DYC.

In triangle AYB, angle a = 40° and angle Y = 90°, to find B,

40° + 90° + B = 180°

130° +  B = 180°

B = 180° - 130°

B = upper half of c = 50°

To find the lower half of c, see triangle DYC.

We know Y = 90°, C = 26° Let's find the lower half of c

D+Y+C = 180

lower half c + 90° + 26° = 180°

c + 116° = 180°

c = 180° - 116°

c = 64°

Now let's add the lower and the upper half of the complete angle c.

50° + 64° = 114°

Therefore angle c = 114°

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