Question

1. Two angles of a triangle are equal and the third angle measures 70 degrees. Find the measure of each of the unknown triangles.
2. One of the acute angles of a right triangle is 36 degrees. Find the other.
3. Find the measure of the angles of a triangle which are in the ratio 4:3:2
4. The acute angles of a right triangle are in the ratio 2:1. Find the measure of each of these angles.

Answer 1

Recall the properties of a triangle.

Q1.

Given:

Two angles are equal. Third angle is $70^\circ$

Sum of angle of a triangle is $180^\circ$

Let the unknown angles be $x$

$\implies x+x+70=180$

$\implies 2x+70=180$

$\implies 2x=180-70$

$\implies 2x=110$

$\implies x=\frac{110}{2}$

$\implies x=55^\circ$

Q2.

Given:

In a right triangle, one angle is $36^\circ$

Let the other angle be $x$

Sum of angle of a triangle is $180^\circ$

$\implies x+36+90=180$

$\implies x+126=180$

$\implies x=180-126$

$\implies x=54^\circ$

Q3.

Given:

The ratio of angle is $4:3:2$

Let the multiplying factor be $x$

Sum of angle of a triangle is $180^\circ$

$\implies 4x+3x+2x=180$

$\implies 9x=180$

$\implies x=\frac{180}{9}$

$\implies x=20$

So the angles are:

$\implies 4x=4(20)=80^\circ$

$\implies 3x=3(20)=60^\circ$

$\implies 2x=2(20)=40^\circ$

Q4.

Given:

The acute angle of a right triangle is in the ratio $2:1$

Let the multiplying factor be $x$

Sum of angle of a triangle is $180^\circ$

$\implies 2x+x+90=180$

$\implies 3x+90=180$

$\implies 3x=180-90$

$\implies 3x=90$

$\implies x=\frac{90}{3}$

$\implies x=30$

So the angles are:

$\implies x=1(30)=30^\circ$

$\implies 2x=2(30)=60^\circ$

Answer 2

Answer:

1. Measure of each of the unknown angle is 55°

2. Measure of the other acute angle is 54°

3. Measure of each angles of the triangle are 80°, 60° and 40°

4. Measure of each acute angles are 60° and 30°

Step-by-step explanation:

1. given, two angles of the triangle are equal and the third angle measures 70 degrees.

Let ∡A = ∡B, and ∡C = 70°

We know, for a triangle, sum of internal angles = 180°

Then, ∡A+∡B+ 70 = 180

∡A+∡B = 180-70 = 110

∡A = ∡B = $\frac{110}{2}$  = 55°

The three angles are 55°, 55°, and 70° respectively

2. given, it is a right triangle

∡A = 90°, ∡B= 36° ∡C = ?

90+36+∡C = 180

∡C = 180-90-36 = 54°

3. given angles are in the ratio 4:3:2

Let the angles be 4x, 3x and 2x

$4x +3x + 2x= 180\\9x = 180\\x = 20$

hence, the angles are: 4×20 = 80°,

3×20 = 60°

and 2×20 = 40°

4. given,  acute angles of a right triangle are in the ratio 2:1

let the acute angles be 2x and 1x

$90 + 2x + 1x = 180\\3x = 180-90 = 90$

$x = \frac{90}{3} = 30$

hence, the acute angles of the triangle are 2x = 2×30 = 60°

and x = 30°