Question

Figure ABCD is a rhombus. Find the value of x.

3x - 13 8x - 7

x = [ ? ]°

Answer 1

`\quad \huge \quad \quad \boxed{ \tt \:Answer }`

`\qquad \tt \rightarrow \: x = 10°`

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`\large \tt Solution \: :`

Diagonals of a Rhombus bisect each other at right angle (90°)

`\qquad \tt \rightarrow \: x + 58 + 90 = 180`

[ Sum of interior angles of a triangle ]

`\qquad \tt \rightarrow \: 3x - 13 + 8x - 7 + 90 = 180`

`\qquad \tt \rightarrow \: 11x + 70 = 180`

`\qquad \tt \rightarrow \: 11x = 180 - 70 \degree`

`\qquad \tt \rightarrow \: 11x = 110`

`\qquad \tt \rightarrow \: x = \cfrac{110}{11}`

`\qquad \tt \rightarrow \: x = 10 \degree`

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer 2

Answer: 10

Explanation:

For simplicity, I will let the intersection of the diagonals be point E.

Since diagonals of a rhombus bisect each other, we know that triangle DEC is a right triangle.

Thus, we can use the fact that the acute angles of a right triangle are complementary to conclude that:

• (3x-13) + (8x-7) = 90 [angles that are complementary add to 90 degrees]
• 11x - 20 = 90 [combine like terms]
• 11x = 110 [add 20 to both sides]
• x = 10 [divide both sides by 11]