Question

PLEASE HELP !!!!! ASAP PLEASE !!!! IM BEGGING LOL !!!!

Answer 1

`\huge\bold{To\:find:}`

✎ The measure of ∠ DBC.

`\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}`

`\sf\purple{The\:measure\:of\:∠DBC\:is\:56°. }`

`\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}`

Since it is right-angle,

`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° = (72°)/(8) \\ ⇢x° = 9°`

Substituting the value of
`x°` in ∠ DBC, we have

`(5x + 11) °\\ = 5 * 9° + 11 °\\ = 45° + 11° \\ = 56°`

`\sf\blue{Therefore,\:the\:measure\:of\:∠DBC\:is\:56°.}`

`\huge\bold{To\:verify :}`

`(3x + 7) ° + (5x + 11)° = 90° \\ \: ➡ \: (3 * 9 + 7)° + (5 * 9 + 11)° = 90° \\ ➡ \: 34° + 56° = 90° \\ ➡ \: 90° = 90° \\ ➡ \: L.H.S.=R. H. S`

Hence verified.

`\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘`

Answer 2

Explanation:

Hey there!

From the given figure;

Angle ABE = 90°.

And angle ABC= [(3x+7)° + (5x+11)°].

Now, Angle ABE + Angle ABC= 180° [Being linear pair].

or, 90° + (3x+7)° + (5x+11)°= 180°

or, (3x+7)° + (5x+11)°= 90°

or, 8x + 18° =90°

or, 8x = 90°-18°

or, X = 9°

Therefore, X= 9°.

Now,

Angle DBC = (5*9+11)°

= 56°

Therefore, the measure of angle DBC is 56°.

Hope it helps!