Question

Find the measure of the arc,

Answer 1

mEDF = 124°

Steps

360 = 146 + 90 + x

360 = 236 + x

-236 -236

124 = x

Answer 2

m(EDF) = 214°

Explanation:

GIVEN :-

• Measure of minor arc FE = 146°
• Measure of minor arc DE = 90°

TO FIND :-

• Measure of major arc FE (also known as arc FDE)

FACTS TO KNOW BEFORE SOLVING :-

• Sum of all angles in a circle is 360°.

SOLUTION :-

According to the figure given in question ; in the orange circle ,

m(minor FE) + m(minor DE) + m(minor FD) = 360°

⇒ 146° + 90° + m(minor FD) = 360°

⇒ m(minor FD) = 360° - 236° = 124°

∴ m(major FE) [or] m(EDF) = m(minor DE) + m(minor FD) = 90° + 124° = 214°