Question

8. In the given figure ZAPB = 105°. Find the measure of the
ZATB
А​

Answer 1

$\mathcal {\orange {SOL:-}}$

∠APB = 105°

∠APB =1/2m(arcAB)

.....inscribed angle

105 × 2 = m(arcAB)

m(arcAB) = 210°

$\tt \red{now,</strong><strong>}</strong><strong> </strong><strong>$

m(arcAB) + m(arcAPB) =360°

....Full circle

210 + m(arcAPB) = 360

m(arcAPB) = 360 - 210

m(arcAPB) = 150°✅

•°• ∠ AOB = m(arcAPB)

....central angle

•°• ∠AOB = 150°

$\tt \red{now,}$

In □TAOB Sum of all angles of quadrilateral is 360°

∠ATB + ∠TBO + ∠AOB +

∠TAO = 360°

∠ATB + 90° + 150° + 90° = 360°

..... {Tangent theorem for 90°}

∠ATB + 330 = 360°

∠ATB = 360 - 330

∠ATB = 30° ✅

$\mathcal {\red {MEASURE \: OF \: ANGLE \: ∠ATB = 30° }}$