Question

Two adjacent angles of a rhombus are in the ratio 4: 5. the measures of adjacent angles are

Answer 1

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Answer 2

$Hi \: \: !!! \\ \\ Here \: \: is \: \: your \: \: answer, \\ \\ As \: \: one \: \:property \: \: of \: \: the \: \: \\ rhombus \: = pair \: \: of \: \: adjacent \: \: \\ sides \: \: are \: \: equal. \\ So, \\ the \: \: adjacent \: \: angles \: \: are \: \: \\ supplementary \: \: angles \: \\ (sum \: \: of \: \: adjacent \: \: angles = 180 \: degree \: ) \\ \\ (ATQ) \\ Two \: \: adjacent \: \: angles \: \: of \: \: a \: \: rhombus \\ \: are \: \: in \: \: ratio \: 4:5 \\ \\ Let \: \: one \: \: angle \: \: be \: \: 4x \\ and \: \: another \: \: angle \: \: be \: 5x \\ \\ angle \: 4x + angle \: 5x = 180 \: degree \\ = > 4x + 5x = 180 \\ = > 9x = 180 \\ = > x = \frac{180}{9} \\ = > x = 20 \\ \\ one \: \: angle \: = 4x = 4 \times 20 = 80 \: \\ another \: \: angle = 5x = 5 \times 20 = 100 \\ \\ Hence, two \: \: adjacent \: \: angles \: are \\ 80 \: degree \: \: and \: \: 100 \: degree \\ \\ \\ Hope \: \: it \: \: helps.$