Advertisements
Advertisements
Question
In ∆LMN, MN is extended to O. If ∠MLN = 100 – x, ∠LMN = 2x and ∠LNO = 6x – 5, find the value of x
Advertisements
Solution
Exterior angle is equal to the sum of the opposite interior angles
∠LNO = ∠MLN + ∠LMN
6x – 5 = 100° – x + 2x
6x – 5 + x – 2x = 100°
6x + x – 2x = 100° + 5°
5x = 105°
x = `(105^circ)/5` = 21°
x = 21°
APPEARS IN
RELATED QUESTIONS
Find the value of the unknown exterior angle x in the following diagram:
Find the value of the unknown interior angle x in the following figure.
∠ACD is an exterior angle of ∆ABC. The measures of ∠A and ∠B are equal. If m∠ACD = 140°, find the measures of the angles ∠A and ∠B.
In the isosceles triangle ABC, ∠A, and ∠B are equal. ∠ACD is an exterior angle of ∆ABC. The measures of ∠ACB and ∠ACD are (3x − 17)° and (8x + 10)°, respectively. Find the measures of ∠ACB and ∠ACD. Also find the measures of ∠A and ∠B.
Find the value of ‘x’ in the given figure
In the following figure, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is ______.
The measures of ∠x and ∠y in the following figure are respectively.
In the following figure,
- ∠TPQ = ∠ _____ + ∠ _____.
- ∠UQR = ∠ _____ + ∠ _____.
- ∠PRS = ∠ _____ + ∠ _____.
In the given figure, ∠PRS = ∠ ______ + ∠ _______
According to the Exterior Angle Rule, the measure of an exterior angle of a triangle is equal to the sum of which two angles?
