2angles of a quadrilateral measures 40degree and 60degree the other 2angles are equalthe the measures of each of these two angles are
Answers
Answer:
The measure of each of the two equal angles is 130°
Step-by-step explanation:
Given :
Two angles of a quadrilateral measure 40° and 60° and the other two angles are equal.
To find :
the measure of each of these two angles
Solution :
Let the measure of each of the two equal angles be x°
Sum of all the four angles in a quadrilateral = 360°
40° + 60° + x° + x° = 360°
100° + 2x° = 360°
2x° = 360° - 100°
2x° = 260°
x = 260/2
x = 130°
∴ The measure of each of the two equal angles is 130°
Verification :
40° + 60° + 130° + 130° = 360°
100° + 260° = 360°
360° = 360°
LHS = RHS
Hence verified!
Solution ↓
→ We know that :-
» Quadilateral angles are those in which sum of 4 angles is 360°.
→ Angle A = 40°
→ Angle B = 60°
→ Angle C = ?
→ Angle D = ?
Let angle C be a, then
angle D also will be a.
→ According to question :-
40° + 60° + a° + a° = 360°
100° + a° + a° = 360°
100° + ay° = 360°
2a = (360 – 100)°
2a = 160°
a = (160 ÷ 2)°
a = 80° (Ans)
Therefore,
Angle C = 80°
Angle D = 80°
Verification ↓
A + B + C + D = 360°
40° + 60° + 80° + 80° = 360°
100° + 80° + 80° = 360°
180° + 80° = 360°
360° = 360°
LHS = RHS
Hence it's verified.