Obtuse Angled Triangle

Q.

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is:

1. A right triangle

2. An isosceles triangle

3. An obtuse angled triangle

4. An equilateral triangle

Q.

The bisectors of the base angles of an isosceles triangle ABC, with AB = AC, meet at O.

If $\angle B=\angle C={50}^{\circ }$. What is the measure of angle O ?

1. 150^o

2. 80^o

3. 130^o

4. 120^o

Q.

Incentre can lie inside, on or outside the triangle.

1. True

2. False

Q. If two acute angles of a right triangle are equal, then each acute is equal to

(a) 30°

(b) 45°

(c) 60°

(d) 90°

Q.

The bisectors of the base angles of an isosceles triangle ABC, with AB=AC, meet at O. If ∠B = ∠C = 50°. What is the measure of angle O?

1. 130^o

2. 150^o

3. 120^o

4. 80^o

Q. If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.

Q. 33. In triangle ABC, segAB = SegA C & P is any points on AC.Through C, a line is drawn to intersect BP produced in Q such that ANGLE ABQ=ANGLE ACQ .Prove that ANGLE AQC=90^° +1/2 ANGLE BAC.

Q. How to prove that a triangle must have atleast two acute angle ?

Q. In the given figure, ∠ABD = 54° and ∠BCD = 43°, calculate (i) ∠ACD (ii) ∠BAD (iii) ∠BDA.

Q. Mark the correct alternative in each of the following:

If all the three angles of a triangle are equal, then each one of them is equal to

(a) 90°

(b) 45°

(c) 60°

(d) 30°

Q. In figure, E and F are mid - points of the sides AB and AC respectively of the $\Delta ABC$. G and H are mid-points of the sides AE and AF respectively of the $\Delta AEF$. If GH =1.8 cm, find BC.

Q. The bisectors of base angles of a triangle cannot enclose a right angle in any case.

Q. In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.

Q. Let U be the set of all triangles in a plane.If A is the set of all triangles with at least one angle different from ${60}^0$, what is A'?

Q. Mark (✓) against the correct answer in each of the following:
In the given figure, ∆ABC is an equilateral triangle and ∆BDC is an isosceles right triangle, right-angled at D. Then ∠ACD = ?
(a) 60°
(b) 90°
(c) 120°
(d) 105°
Figure

Q. In the figure given, the measure in degrees of $\angle ABC$ is ${72}^{\circ }$. Find the value of $x$.

1. ${18}^{\circ }$
2. ${24}^{\circ }$
3. ${27}^{\circ }$
4. ${30}^{\circ }$

Q.

A triangle can have:

1. All angles more than 60^o

2. Two obtuse angles

3. Two acute angles

4. Two right angles

Q. Which of the following triangles have their one side as an altitude?

1. Obtuse angled triangle
2. Acute angled triangle
3. Equilateral triangle
4. Right angled triangle

Q.

An obtuse-angled triangle is one in which all the angles are less than 90°

1. True
2. False

Q. An triangle has one obtuse angle and two acute angles.

1. acute-angled
2. obtuse-angled
3. reflex-angled
4. right-angled

Q. The vertical angle of an isosceles triangle is 100°. Find its base angles.

Q.

Where does the centre of circumcircle of an obtuse triangle lie?

1. Inside the triangle

2. Outside the triangle

3. Can't say.

4. On the side of triangle

Q. Atmost how many obtuse angle(s) can we have in a triangle?

1. 2
2. 1
3. 0
4. 3

Q. State whether the following statements are true (T) or false (F):
A triangle can have all three angles with a measure of less than $60°$.

1. True
2. False

Q. If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

Q. Find the value of unknowns $x$ and $y$ in the following diagrams:

Q. In a right-angled triangle, one of the acute angles measures 53°. Find the measure of each angle of the triangle.

Q. In triangle $ABC,\overline{AB}=\overline{AC}$, angle $A={40}^{\circ }$. point $O$ is within the triangle with angle $OBC$ = angle $OCA$. The number of degrees in angle $BOC$ is :

1. $110$
2. $35$
3. $140$
4. $55$
5. $70$

Q.

In figure, E and F are mid - points of the sides AB and AC respectively of the $\Delta ABC$. G and H are mid-points of the sides AE and AF respectively of the $\Delta AEF$. If GH =1.8 cm, find BC.

1. 7.2cm
2. 9cm
3. 8.2cm
4. 7.6cm