Advertisements
Advertisements
Question
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
Options
94°
54°
40°
44°
Advertisements
Solution
the given problem, the exterior angles obtained on producing the base of a triangle both ways are 94°and 126°. So, let us draw ΔABC and extend the base BC, such that:
∠ACD = 126°
∠ABE = 94°
Here, we need to find ∠BAC
Now, since BCD is a straight line, using the property, “angles forming a linear pair are supplementary”, we get
∠ AC+ ∠ ACD = 180°
∠ ACB + 126° = 180°
∠ ACB = 180° - 126°
∠ ACB = 54°
Similarly, EBS is a straight line, so we get,
∠ ABC + ∠ ABE = 180°
∠ ABC + 94° = 180°
∠ ABC = 180° - 94°
∠ ABC = 86°
Further, using angle sum property in ΔABC
∠ ABC + ∠ ACB + ∠ BAC = 180°
54° + 86° + ∠ BAC = 180°
∠ BAC = 180° - 140°
∠ BAC = 40°
Thus, ∠ BAC = 40°
APPEARS IN
RELATED QUESTIONS
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
- OB = OC
- AO bisects ∠A
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.
Write the sum of the angles of an obtuse triangle.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In the given figure, what is z in terms of x and y?
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
Which of the following correctly describes the given triangle?
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = AC].
