Question

Find the measure of all the angles formed by the

Answer 1

Hint: The lines which do not intersect each other at any point that they do not meet even when they are extended to infinity are called parallel lines. In the given question, we have two horizontal lines that are parallel to each other and are cut by a diagonal line. The diagonal is also called transversal; it is defined as the line which meets two or more parallel lines. There are several properties of angles associated with parallel lines, for example a pair of corresponding angles or alternate interior angles or alternate exterior angles are equal. Using one of these properties we can find out the correct answer of the given question.

Complete step-by-step answer:
The angles that are given in the figure form a pair of alternate interior angles and we know that alternate interior angles are equal, so –
 $
  (4x + 5)^\circ = (3x + 10)^\circ \\
   \Rightarrow 4x + 5 = 3x + 10 \\
  4x - 3x = 10 - 5 \\
   \Rightarrow x = 5 \;
  $
Thus, $ (4x + 5)^\circ = (4 \times 5 + 5)^\circ = 25^\circ $ and $ (3x + 10)^\circ = (3 \times 5 + 10)^\circ = 25^\circ $
Putting the value of x in the given angles, we get the measure of the angles equal to $ 25^\circ $

So, the correct answer is “ $ 25^\circ $ ”.

Note: In geometry, a line is the combination of points to infinity. A line is of mainly 5 types - Vertical lines, horizontal lines, diagonal lines, zigzag lines and curved lines. The lines can be thick and thin depending on the dimensions. Only horizontal, vertical and diagonal lines are straight lines. In the given question, there are two horizontal lines, and one diagonal line cutting both the lines. The diagonal line is a straight line which makes an angle with a horizontal or vertical.