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faltersainse [42]
2 years ago
14

Helloo!!! please help me on this !!!!

Mathematics
1 answer:
ivann1987 [24]2 years ago
7 0

It is given that ️PQR & ️UVW are congruent to each other. According to CPCT, the corresponding angles in 2 triangles willl have the same measure. So, ∠R = ∠W, i.e, (10x - 18)° = 8x°

\mathfrak{10x - 18 = 8x}

\mathfrak{10x - 8x = 18}

\mathfrak{2x = 18}

\mathfrak{x = \dfrac{18}{2}}

\underline{\mathfrak{x = 9}}

Measure of ∠R :

\mathfrak{8x}

\mathfrak{8(9)}

\boxed{\mathfrak{72^{\circ}}}

 ღ ꪑ꠸᥅ꫀꪊ

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<h2>\large\mathfrak{{\pmb{\underline{\red{Given}}{\red{:}}}}}</h2>
  • ∠RSU and ∠USV are complementary angles
  • ∠RSU = (4x – 15)°
  • ∠USV = 20°

<h2>\large\mathfrak{{\pmb{\underline{\color{red}{To~find}}{\color{red}{:}}}}}</h2>
  • The value of x

<h2>\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}</h2>
  • ∠RSU and ∠USV are complementary angles

\sf\implies{ \angle RSU + \angle USV = 90 \degree }

\sf\implies{ (4x-15) + 20 = 90 }

\sf\implies{ 4x-15+20=90}

\sf\implies{4x+5=90}

\sf\implies{4x=90-5}

\sf\implies{4x=85}

\sf\implies{x={\dfrac{85}{4}}}

\sf\implies{ {\orange{\underline{\boxed{\sf{\pmb{x=21.25}}}}}}}

<h2>\large\mathfrak{\therefore{\pmb{\underline{\color{gold}{Required~answer}}{\color{gold}{:}}}}}</h2>
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