use kite defg and the given information to solve #25 - 26.
25) if mz1 = 42° , find m22.
26) if de = 4x – 2 and dg = 22.5, find the value of x.
use kite abcd and the given information to solve #27.
27) find the value of x.

25). Measure of angle 2 will be 48°.

26). Value of x = 6.125

27). Value of x = 56°

25). Given in the picture,

     Apply triangle sum theorem in ΔEHF,

     m∠EHF + m∠2 + m∠1 = 180°

     90° + m∠2 + 42° = 180°  [Since, m∠EHF = 90°]

     m∠2 = 180° - 132°

     m∠2 = 48°

            Therefore, measure of angle 2 will be 48°.

26). Given in the question,

    By the property of a kite,

    DE = DG

    (4x - 2) = 22.5

    4x = 24.5

    x = 6.125

           Therefore, value of x will be 6.125

27). Given in the question,

    Sum of the interior angles of a kite = 360°

    Therefore, m∠A + m∠B + m∠C + m∠D = 360°

    By the property of a kite,

    m∠A = m∠C = 82°

    m∠A + m∠B + m∠A + m∠D = 360°

    2(m∠A) + m∠B + m∠D = 360°

    2(82°) + 140° + x° = 360°

     x = 360° - 304°

     x = 56°

          Therefore, value of 'x' will be 56°.

Learn more about the properties of a kite here,

link

see explanation

Step-by-step explanation:

25

The diagonals of a kite are perpendicular to each other, hence

∠EHF = 90°

The sum of the 3 angles in a triangle = 180°

In ΔEHF

∠1 + ∠2 + 90 = 180, that is

42 + ∠2 + 90 = 180

132 + ∠2 = 180 ( subtract 132 from both sides )

∠2 = 48°

26

DE and DG are congruent sides, hence

4x - 2 = 22.5 ( add 2 to both sides )

4x = 24.5 ( divide both sides by 4 )

x = 6.125

27

∠A and ∠C are congruent, hence

∠A = ∠C = 82°

The sum of the interior angles of a kite = 360°, hence

x = 360 - (82 + 82 + 140) = 360 - 304 = 56