[tex]\huge\bold{To\:find:}[/tex]
✎ The measure of ∠ DBC.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\sf\purple{The\:measure\:of\:∠DBC\:is\:56°. }[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Since it is right-angle,
[tex]Sum \: of \: angles \: = 90° \\ ⇢ (3x + 7)° + (5x + 11) ° = 90° \\ ⇢3x° + 7° + 5x° + 11° = 90° \\combining \: the \: like \: terms, \: we \: have \\ ⇢3x° + 5x° + 7° + 11° = 90° \\ ⇢8x° = 90° - 18° \\ ⇢8x° = 72° \\ ⇢x° = \frac{72°}{8} \\ ⇢x° = 9°[/tex]
Substituting the value of [tex]x°[/tex] in ∠ DBC, we have
[tex](5x + 11) °\\ = 5 \times 9° + 11 °\\ = 45° + 11° \\ = 56°[/tex]
[tex]\sf\blue{Therefore,\:the\:measure\:of\:∠DBC\:is\:56°.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex](3x + 7) ° + (5x + 11)° = 90° \\ \: ➡ \: (3 \times 9 + 7)° + (5 \times 9 + 11)° = 90° \\ ➡ \: 34° + 56° = 90° \\ ➡ \: 90° = 90° \\ ➡ \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]