Question

If a is 95,what is $b + d - e$?

A. 95
B. 85
C. 65
D. 45

Answer 1

Hint: Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other. Vertical angles are always equal to one another. The angles a and d are vertical opposite each other on the line.

Complete step by step solution:
So here, $a = 95$.
The equation is given as, $b + d - e$.
In the given figure that is, $a = d$, $b = e$ and $c = f$. The given equation $b + d - e$ now becomes $b + d - b$ which yields d. So, we need to get the value of d.
So, a and d are vertical angles. They have the same measures as $a = d = 95$.
Since, b and e are vertical angles. They have the same measures as $b = e$.
$\eqalign{
  & \Rightarrow b + d - e \cr
  & \Rightarrow b + d - b \cr
  & \therefore b + 95 - b = 95 \cr} $.

Thus, the option (A) is correct.

Note: If the angles are formed from two intersecting lines and the angles are not adjacent then the pair of angles is said to be vertical. The intersecting lines (two or more) meet only at one point always. The two angles share a common vertex. The intersecting lines can cross each other at any angle. This angle formed is always greater than $0^\circ $ and less than $180^\circ $. Such angles can be known as congruent as angles are equal in measure.