Figure ABCD is a rhombus. Find the value of x. 3x - 13 8x - 7 x = [ ? ]°

Question

asked Oct 21, 2023 146k views

2 Answers

Niels Mouthaan · Answer 1 · 2023-10-22T14:01:23+0000

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

$\qquad \tt \rightarrow \: x = 10°$

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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 ❞

RubesMN · Answer 2 · 2023-10-27T19:07:24+0000

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: