What is the measure of STY in O below
2 answers:
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Answer:
∠HGJ = 35°
Step-by-step explanation:
Although the question is somewhat incomplete, I have tried to reconstruct the question as much as possible to aid understanding (attached is the pictorial representation of the rhombus).
Firstly, it is important to note that rhombuses are parallelograms which have all sides equal and whose diagonals are perpendicular to each other. In addition to this, their diagonals bisect one other.
Mathematically, |EF| = |FG| = |GH| = |HE|
Another property which rhombuses have is that their opposite angles are equal.
Mathematically, ∠E = ∠G, ∠H = ∠F
The adjacent angles in a rhombus are supplementary. This means that the sum of angles closest to each other is 180°.
Mathematically, ∠E + ∠F = 180°, ∠F + ∠G = 180°, ∠G + ∠H = 180°,
∠H + ∠E = 180°
The question gave us ∠GHE and asked us to find ∠HGJ (denoted as θ in the picture attached). Note that ∠GHE means ∠H. That is, ∠GHE ⇒ ∠H
∠GHE or ∠H = 110°
From the properties of rhombuses (earlier stated), we know that adjacent angles in a rhombus are supplementary
Mathematically,
∠GHE + ∠FGH ⇒ 110° + ∠FGH = 180° ⇒ ∠FGH = 180° - 110°
∠FGH or ∠G = 70°
To calculate for ∠HGJ, we divide ∠FGH by 2, we have:
∠HGJ = ∠FGH ÷ 2 = 70° ÷ 2
∠HGJ = 35°
Use <em>CPCTC</em> and make ratios and proportionalities to find the value of segment PW:
If △WPJ∼△DNJ, then according to CPCTC, WP must be proportional to DN and PJ must be proportional to JN. Now, we can make a ratio:
Substitute the values that are given in the diagram.
DN=87.5
NJ=56
PJ=64
Solve for x. You can do it by cross-multiplication.
The measure of segment WP is 100 meters.
If △WPJ∼△DNJ, then according to CPCTC, WP must be proportional to DN and PJ must be proportional to JN. Now, we can make a ratio:
Substitute the values that are given in the diagram.
DN=87.5
NJ=56
PJ=64
Solve for x. You can do it by cross-multiplication.
The measure of segment WP is 100 meters.