An angle exceeds its complement by 24°. Find the angle.

Class 7Lines and AnglesLines and Angles

A33°
B66°
C114°
D57°

Step-by-Step Solution

Let the angle be

x

, so its complement is

90 - x

. Then

x - (90 - x) = 24

→

2 x - 90 = 24

→

2 x = 114

→

x = 57

°. Check: complement = 33°, and 57 − 33 = 24. Trap: 33° is the complement, not the angle asked for; 114° is

2 x

left un-halved; 66° comes from just doing 90 − 24.

Answer: D) 57°

Key idea: Solving 'find the angle' problems

Most Class-7 angle problems give you one or two angle measures and ask you to find an unknown one. The recipe:

1. Identify the relationship: vertically opposite? linear pair? corresponding? alternate?
2. Write an equation: equal-to or sum-to-180.
3. Solve for the unknown.
4. Mark it back on the diagram and sanity-check (acute should look acute, obtuse should look obtuse).

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