In ΔABC, if ∠A = 70° and ∠B = 70°, find the measure of exterior angle A.
110°
To find the measure of the exterior angle A in ΔABC, we need to understand the properties of angles in a triangle and their relationship to exterior angles.
Step 1: Calculate the measure of ∠C in ΔABC. The sum of interior angles in any triangle is always 180°. Therefore, ∠C can be found using the equation:
∠A + ∠B + ∠C = 180°
Given that ∠A = 70° and ∠B = 70°, we can substitute these values into the equation:
70° + 70° + ∠C = 180°
140° + ∠C = 180°
Subtract 140° from both sides to solve for ∠C:
∠C = 40°
Step 2: Determine the measure of exterior angle A. An exterior angle in a triangle is equal to the sum of the opposite interior angles, which are ∠B and ∠C in this case.
Exterior Angle A = ∠B + ∠C
Substitute the known values:
Exterior Angle A = 70° + 40° = 110°
Therefore, the measure of exterior angle A is 110°. This matches the provided correct answer choice.
Important Questions from Triangles
What is the foot of the altitude from the vertex A of the triangle ABC?
Two poles, 15 m and 30 m in height, stand upright in a playground. If their feet are 36 m apart, then find the distance between their tops.
How many triangles are there in the given figure?
How many triangles are there in the given figure?
Find the area (in square cm) of a right angled triangle whose altitude is 7 cm less than its base and its hypotenuse is 17 cm.
