Alternatives of Postulate 5

Q.

If the angles of a triangle are in the ratio 2 : 3 : 5, the triangle is ___

1. acute angled

2. obtuse angled

3. Equilateral

4. Right angled

Q. The three angles of a triangle are in the ratio 1 : 2 : 3. What is the largest angle in the triangle?

1. 30${}^{\circ }$
2. 90${}^{\circ }$
3. 60${}^{\circ }$
4. 120${}^{\circ }$

Q. The angles of a triangle are in the ratio 1 : 1 : 2. What is the largest angle in the triangle?

1. 90${}^{\circ }$
2. 150${}^{\circ }$
3. 135${}^{\circ }$
4. 45${}^{\circ }$

Q.

A triangle ABC is right angled at A. AL is drawn perpendicular to BC. Prove that $\angle$ BAL = $\angle$ACB.

Q. In the given figure, if $\angle$ABC = 60 ${}^{\circ }$, $\angle$CAB = 60 and BD is a straight line, ${}^{\circ }$, what is the value of 2 $\angle$ACD?

1. 120 ${}^{\circ }$
2. 150 ${}^{\circ }$
3. 240 ${}^{\circ }$
4. 100 ${}^{\circ }$

Q. If the angles of a triangle are in the ratio 2 : 3 : 4, what is the difference between the largest angle and the smallest angle?

1. 20${}^{\circ }$
2. 60${}^{\circ }$
3. 80${}^{\circ }$
4. 40${}^{\circ }$

Q.

In the following, the set of measures which can form a triangle

1. , ,

2. , ,

3. , ,

4. , ,

Q.

Question 2
In the given figure sides AB and AC of $\Delta$ABC are extended to points P and Q respectively. Also, $\angle PBC<\angle QCB$. Show that AC > AB.

Q. In a triangle ABC , it is known $\angle$A = 45 ${}^{\circ }$ and $\angle$B = 75 ${}^{\circ }$. What is the value of $\angle$C ?

1. 65 ${}^{\circ }$
2. 45 ${}^{\circ }$
3. 55 ${}^{\circ }$
4. 60 ${}^{\circ }$

Q. In a triangle ABC , it is known, $\angle$A = 60 ${}^{\circ }$, $\angle$B = 90${}^{\circ }$. What is the value of $\angle$ACE?

1. 160 ${}^{\circ }$
2. 120 ${}^{\circ }$
3. 150 ${}^{\circ }$
4. 30 ${}^{\circ }$

Q.

Geometry The measure of one acute angle in a right triangle is four times the measure of the other acute angle.

Write and solve a system of equations to find the measures of the acute angles.

Q. In the figure, if $AB\parallel DE,\angle BAC={35}^o$ and $\angle CDE={53}^o$, find $\angle DCE$.

Q. If $\angle$ACD = 120${}^{\circ }$ and $\angle$B = 20${}^{\circ }$, what is the value of $\angle$BAC?

1. 120${}^{\circ }$
2. 160${}^{\circ }$
3. 140${}^{\circ }$
4. 100${}^{\circ }$

Q.
What is the value of $\angle$A + $\angle$B + $\angle$C + $\angle$D + $\angle$E + $\angle$F ?

1. 150${}^{\circ }$
2. 180${}^{\circ }$
3. 270${}^{\circ }$
4. 360${}^{\circ }$

Q. In the figure, AB||CD||EF and GH||KL. Find $\angle HKL$.

1. ${165}^0$
2. ${60}^0$
3. ${145}^0$
4. ${120}^0$

Q.
In the figure, it is known , $\angle$CBA = 60 ${}^{\circ }$ and $\angle$BCA = 40 ${}^{\circ }$. What is the value of $\angle$CAO ?

1. 120 ${}^{\circ }$
   
2. 80 ${}^{\circ }$
   
3. 100 ${}^{\circ }$
   
4. 60 ${}^{\circ }$

Q. Find the measure of the missing angle in the triangle below.

1. ${35}^o$
2. ${50}^o$
3. ${45}^o$
4. ${40}^o$
5. ${55}^o$

Q. In the following figure,

$\angle$1 = 50${}^{\circ }$, $\angle$2 = 80${}^{\circ }$, $\angle$3 = 70${}^{\circ }$ and
$\angle$4 = 60${}^{\circ }$. What is the value of $\angle$5 +$\angle$6?

1. 120${}^{\circ }$
2. 80${}^{\circ }$
3. 90${}^{\circ }$
4. 100${}^{\circ }$

Q.
In the given figure, it is known, L1$\parallel$ L2 and $\angle$EBC = 130${}^{\circ }$ and $\angle$ACD = 60${}^{\circ }$. What is the value of $\angle$ACB?

1. 40${}^{\circ }$
2. 60${}^{\circ }$
3. 70${}^{\circ }$
4. 50${}^{\circ }$

Q.
In the above figure, what is the value of
$\angle$1 + $\angle$2 + $\angle$3 + $\angle$4 ?

1. 210${}^{\circ }$
   
2. 180${}^{\circ }$
   
3. 150${}^{\circ }$
4. 120${}^{\circ }$
   

Q. Which of the following is/are true?

1. The sum of angles of any triangle is a constant and is equal to
   two right angles.
2. Straight lines parallel to the same straight line are parallel to one another.
3. All right angles are not equal to one another.
4. There is a unique line that passes through a given point.

Q. In the above figure, BE $\parallel$ OD and $\angle$ACB = 45${}^{\circ }$ and $\angle$BAC = 60${}^{\circ }$. What is the value of $\angle$BOD?

1. 145 ${}^{\circ }$
2. 90 ${}^{\circ }$
3. 135 ${}^{\circ }$
4. 75 ${}^{\circ }$

Q. Prove that equilateral triangle is equiangular.

Q.

In a $∆\mathrm{ABC}$, $\angle A+\angle B=144°$ and $\angle A+\angle C=124°$ then $\angle B=$

1. $56°$

2. $60°$

3. $65°$

4. $45°$

Q. The measure of $\angle x$ in degrees is

Q.

In the given figure, lines (i) and (ii) are parallel lines and $AC$ is the angle bisector of $\angle BAD$.

What type of triangle is $△ABC$?

1. Equilateral Triangle

2. Acute Angled Triangle

3. Isosceles Triangle

4. Scalene Triangle

Q. In a quadrilateral $ABCD,CO$ and $DO$ are the bisectors of $\angle C$ and $\angle D$ respectively. Prove that $\angle COD=\frac{1}{2}(\angle A+\angle B)$

Q. In the two given triangles, find the value of $\angle R$ if Triangle ABC is similar to PQR

1. ${60}^o$
2. ${70}^o$
3. ${80}^o$
4. None of the above

Q. In the figure, if $AB\parallel CD,CD\parallel EF$ and $y:z=3:7$, find $x$.

Q. In a $△ABC$, the lengths of the two larger sides are $10$ and $9$ units, respectively. If the angles are in A.P, then the length of the third side can be

1. $5\pm \sqrt{6}$
2. $3\sqrt{3}$
3. $5$
4. None of these