Question

a) Work out the size of angle x.
b) Give reasons for your answer. Clearly identify the angles you find and the reasoning (eg. + Angle ABC... because...)

​all help appreciated ty <3

Answer 1

a) 75°

b) when a transversal cuts through two parallel lines,the angles formed on the exterior of either of its sides add up to 180° and are called, 'co-exterior angles'.

thus,

• m∠ABC + m∠EFG = 180°
• m∠ABC = 180° - m∠EFG

plugging in the value,

• x + 105° = 180°
• x = 180° - 105°
• x = 75°

therefore, the value of x = 75°.

Answer 2

Answer:

a. $x = \boxed{\, 75 \, }^\circ$

b. Because $\angle ABC \textsf{ and } \angle EFG$ are co-exterior angles and they are supplementary.

Step-by-step explanation:

To solve the size of angle $x$, we'll need to use the concept of co-exterior angles.

a) To find the size of angle $x$, we'll start by recognizing that the sum of co-exterior angles is 180°.

Given:

$\angle EFG = 105^\circ$ (co-exterior angle to angle $x$)

b) Now, we can set up an equation to find angle $x$:

$\begin{aligned} \sf \angle EFG + \angle ABC &= 180^\circ \quad \textsf{(Sum of angles of a co-exterior angle are supplementary)} \\\\ 105^\circ + x &= 180^\circ \\\\ x &= 180^\circ - 105^\circ \\\\ x &= 75^\circ\end{aligned}$

a) Therefore, the size of angle $x$, or $\angle ABC$ is $75^\circ$.

b) Reasons:

$\angle ABC = 75^\circ$ because $\angle ABC \textsf{ and } \angle EFG$ are co exterior angles and they are supplementary.