Question

Please help me .Give answer of the above question. ​

Answer 1

Answer:

angle RST will be equal to 55 degrees

Step-by-step explanation:

angle subtended at the centre is double the angle formed by the two line segments at the middle

hope this helps

Answer 2

QUESTION :-

In ΔRST , measure of angle ∠RPT = 110° and ∠SRP = ∠PRT as well as ∠STP = ∠PTR = y . Then find the measure of the ∠RST.

GIVEN :-

• ∠SRP = ∠PRT = x°
• ∠STP = ∠PTR = y°
• ∠RPT = 110°

TO FIND :-

• Measure of ∠RST

SOLUTION :-

∠SRT = ∠SRP + ∠PRT = x + x = 2x

∠STR = ∠STP + ∠PTR = y + y = 2y

Consider ΔPRT ,

Using angle sum property ,

$\implies \bf \angle \: PRT+ \angle \: PTR + \angle \: RPT \\ \\ \implies \bf\: x + y + 110 {}^{\circ} = 180 {}^{\circ} \\ \\ \implies \bf\: x + y = 180 {}^{\circ} - {110}^{\circ} \\ \\ \implies \underline {\boxed {\pink {\bf{x + y = 70 {}^{\circ} }}}} \longrightarrow \: eq(1)$

Consider ΔSRT ,

using angle sum property ,

$\implies \bf\angle SRT + \angle STR + \angle RST = 180 {}^{\circ} \\ \\ \implies \bf \: 2x + 2y + \angle RST = 180 {}^{\circ} \\ \\ \implies \bf\: 2(x + y) + \angle RST = {180}^{\circ}$

From eq(1) ,

$\implies \bf\: 2(70) + \angle RST = {180}^{\circ} \\ \\ \implies \bf \: 140 {}^{\circ} + \angle RST = {180}^{\circ} \\ \\ \implies \bf \: \angle RST = {180}^{\circ} - {140}^{\circ} \\ \\ \implies {\underline {\boxed {\blue {\bf{ \: \angle RST = 40 {}^{\circ} }}}}}$

∴ The measure of ∠RST in given triangle is 40°