Advertisements
Advertisements
Question
∠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.
Advertisements
Solution
Let the measures of ∠A be x°.
m∠A = m∠B = x°
∠ACD is the exterior angle of ∆ABC
∴ m∠ACD = m∠A + m∠B
∴ 140° = x + x
∴ 140° = 2x
∴ 2x = 140°
∴ x = `140^circ/2`
= 70°
∴ The measures of the angles ∠A and ∠B are 70°, respectively.
RELATED QUESTIONS
Find the value of the unknown exterior angle x in the following diagram:
Using the measures of the angles given in the figure alongside, find the measures of the remaining three angles.
If an exterior angle of a triangle is 115° and one of the interior opposite angles is 35°, then the other two angles of the triangle are
From the given figure, the value of x is ______.
In ∆PQR, if ∠P = 60°, and ∠Q = 40°, then the exterior angle formed by producing QR is equal to ______.
In the following figure, if AB || CD, then ______.
In ∆ABC, ∠Α = 50°, ∠B = 70° and bisector of ∠C meets AB in D (see figure). Measure of ∠ADC is ______.
In the given figure, ∠UQR = ∠______ + ∠ ______
In ∆ABC, if ∠A = ∠C, and exterior angle ABX = 140°, then find the angles of the triangle.
In the following figure, if y is five times x, find the value of z.
