Question

Use the diagram below to find each labelled angle.
A. 32°
B. 64°
C. 24°
D. 48°

Answer 1

$\large \underline{\pink{\pmb{\mathfrak{Given....}}}}$

We are given a figure having two angles $\bf 6x\degree$ and $\bf (4x+8)\degree$ formed at the intersection of two lines.

$\large \underline{\pink{\pmb{\mathfrak{To~ find....}}}}$

We have to find the value of x and the angles.

$\large \underline{\pink{\pmb{\frak{Solution....}}}}$

• In the figure, we see that two lines are interesting each other at a point.
• At the point, two angles have been formed.
• We see that these are vertically opposite to each other.
• We know that vertically opposite angles are equal to each other.

________________________________

$\pmb{\sf{\green{According~ to ~the~ question :}}}$

$\bf : \implies6x \degree = (4x + 8) \degree$

$\pmb{\sf{\green{Solving~ the~ above ~equation :}}}$

$\bf : \implies6x = 4x + 8$

$\bf: \implies6x - 4x = 8$

$\bf: \implies 2x = 8$

$\bf: \implies x = \dfrac{8}{2}$

${\red{ :\implies\bf x = 4 \degree}}$

________________________________

$\pmb{\sf{\green{Substituting}}}~{ \bf x=4°}~\pmb{\sf{\green{in ~the ~angles :}}}$

$\green{\odot }\: \: \bf6x \degree = 24 \degree$

$\green{ \odot} \: \: \bf(4x + 8) \degree = 24 \degree$

$\green{\odot}$ Hence, the angles are $\bf 24° (OptionC)$.