Given: e, f, q, d∈k(o),

o ∈ ed , m∠dfq = 10°,

m ef = 28°

find: angles of △efq

The angles are m∠EQF=14°, m∠EFQ=90° and m∠QEF=76°  

Step-by-step explanation:

Given the figure in which m∠DFQ = 10°,  m∠EOF = 28°

we have to find the angles of △EFQ

m∠EOF = 28°

By theorem angle subtended at the centre is twice the angle subtended at the circumference

⇒ m∠EQF=14°

As angle ∠EFQ is the angle in the semicircle

∴ ∠EFQ=90°

In ΔEFQ, by angle sum property of triangle

m∠EFQ+m∠FQE+m∠QEF=180°

90°+14°+m∠QEF=180°

m∠QEF=180°-90°-14°=76°

Hence,  m∠EFQ=90° and m∠QEF=76°

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