Q. 1325.0( 2 Votes )
In Δ DEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find
(i) ∠F
(ii) ∠EOF.
Answer :
Given: ∠D = 60°, ∠E = 70°
Formula Used/Theory:-
→ Angle sum property
Sum of all angles of triangle is 180°
In Δ DEF
∠D + ∠E + ∠F = 180°
60° + 70° + ∠F = 180°
∠F = 180° - 130° = 50°
Bisector of ∠E will be 35°
Bisector of ∠F will be 25°
Joining the bisector of ∠E and ∠F at O will make a Δ EOF
Where ∠OEF = 35°
And ∠OFE = 25°
By angle sum property
∠OEF + ∠OFE + ∠EOF = 180°
∠EOF + 35° + 25° = 180°
∠EOF = 180° - 60° = 120°
Result:- ∠EOF = 120°
∠F = 50°
Rate this question :
In a right-angled triangle, the angles other than the right angle are
NCERT - Exemplar MathematicsIn Fig. 6.34, find the measures of ∠PON and ∠NPO.
Find the values of x and y in Fig. 6.37. Plan a Strategy
In Δ ABC, if ∠A = ∠C, and exterior angle ABX = 140°, then find the angles of the triangle.
NCERT - Exemplar MathematicsIn a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.
NCERT - Exemplar MathematicsIn Fig. 6.31(i) and (ii), find the values of a, b and c.
In Fig. 6.30, find the value of x.
The measure of three angles of a triangle are in the ratio 5 : 3 : 1. Find the measures of these angles.
NCERT - Exemplar Mathematics