DA = 13, BW = 5, WC = 12, ∠ACD = 25°, ∠DAB = 50°, ∠ADC = 130°, ∠DBC = 65° and ∠BWC = 90° given that ABCD is a rhombus and DB = 10, BC = 13, ∠WAD = 25°. This can be obtained by understanding the properties of a rhombus.
<h3>What are the required values of sides and angles?</h3>
Here in the question it is given that,
- DB = 10, BC = 13, ∠WAD = 25°
We have to find the values of DA, BW, WC, ∠BAC, ∠ACD, ∠DAB, ∠ADC, ∠DBC, ∠BWC.
1) Since all the sides of the rhombus are equal, DA = 13
2) Since diagonals are perpendicular bisectors of each other, BW = 5
3) Since formula of diagonal is,
d₁ = √4a² - d₂,
here a = 13, d₂ = 10
d₁ = √4×13² - 10
d₁ = √676 - 10 = √576 = 24
Since diagonals are perpendicular bisectors of each other
WC = 24/2 ⇒ WC = 12
4) Since diagonals are angle bisectors at the corners, ∠BAC = 25°
5) Since diagonals are angle bisectors at the corners,
∠BAW = ∠DAW = 25° ⇒ ∠BAD =∠BAW + ∠DAW = 25° + 25° ⇒∠BAD = 50°
Since opposite angles of the rhombus are equal,
∠BAD = ∠BCD = 50° ⇒ ∠BCW = ∠DCW = 25°
⇒ ∠ACD = 25°
6) Since diagonals are angle bisectors at the corners,∠BAW = ∠DAW = 25° ⇒ ∠BAD =∠BAW + ∠DAW = 25° + 25° ⇒∠BAD = 50°
⇒ ∠DAB = 50°
7) Since adjacent angles are supplementary angles,
∠BAD + ∠ADC = 180° ⇒ 50° + ∠ADC = 180° ⇒ ∠ADC = 180° - 50° = 130°
⇒ ∠ADC = 130°
8) Since diagonals are angle bisectors at the corners,
∠DBC = 130°/2
⇒ ∠DBC = 65°
9) Since all the sides make an angle of 90° at the center,
⇒ ∠BWC = 90°
Hence DA = 13, BW = 5, WC = 12, ∠ACD = 25°, ∠DAB = 50°, ∠ADC = 130°, ∠DBC = 65° and ∠BWC = 90° given that ABCD is a rhombus and DB = 10, BC = 13, ∠WAD = 25°.
Learn more about rhombus here:
brainly.com/question/27870968
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