Question

Triangle PQR is an isosceles triangle with PQ=PR. If angle Q=70 degree . then the other angles of triangle are

Answer 1

Answer:

55 degree

Step-by-step explanation:

in an isosceles triangle 2 angles and sides are equal

angle P +angle +Q + angle R =180 degree (angle sum )

=70 + angle P +angle Q = 180

=70 + 2 angle P = 180

=2angle P=180-70

=2angle P =110 degree

=angle P=110/2=55degree

therefore the other angles of the triangle are both 55 degree each

Answer 2

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf P }\put(0.5,-0.3){ \bf Q }\put(5.2,-0.3){ \bf R }\end{picture}$

Given:

• ∠PQR = 70°
• PQ = PR

To find:

• ∠PRQ = ?

• ∠QPR = ?

Method:

Important Concepts:

1. Angles opposite to Equal sides are equal
2. Sum of all angles in any triangle is always 180°. This is known as Angle Sum Property

Since PQ = PR,

∠PRQ = ∠PQR = 70°

∴ ∠PRQ = 70°

Applying Angle Sum Property,

∠P + ∠Q + ∠R = 180°

⇒ ∠P + 70° + 70° = 180°

⇒ ∠P + 140° = 180°°

⇒ ∠P = 180° - 140°

⇒ ∠P = 40°

∴ ∠QPR = 40°