Find the angle?
3 Answers
Explanation:
#OP=OSto("radii of circle")#
#rArrtrianglePOS" is isosceles"#
#rArrangleSPO=anglePSO=48^@#
#rArranglePOS=(180-48-48)^@=84^@#
#"angle at centre "=2xx"angle at circumference"#
#rArranglePMS=84^@/2=42^@#
#trianglePMS" is isoceles "to(MP=MS)#
#rArrangleMSP=(180-42)^@/2=69^@#
#rArrangleMSO=69-48=21^@#
#anglePSR=90-48=42^@to("tangent/radius")#
#rArrangleMSR=21+48+42=111^@#
#rArrangleMST=180-111=69^@to("straight angle")#
Explanation:
Calling
Now
Please read the explanation.
Explanation:
In an isosceles triangle, exactly two sides are congruent to each other.
The two angles that lie opposite to the two congruent sides of the isosceles triangle would also be congruent.
In other words, an isosceles triangle would have two congruent base angles.
This is called the isosceles triangle base angle theorem.
Hence,
We already know that the angles in a triangle add up to 180°.
Hence,
The angle formed at the center of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points.
Hence, the angle subtended by an arc at the center is twice the angle subtended at the circumference.
Hence,
Also,
Hence,
A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent.
Hence,
This above diagram shows the alternate segment theorem.
In short, the red angles are equal, and the green angles are equal.
Also,
Please find the solution sketch below: [ NOT drawn to scale. ]
Hope you find this solution useful.
