Question

*One of the angles of a triangle is 75°. If the difference of the remaining two angles is 35°, then the largest angle of the triangle has a measure of ____.*

1️⃣ 75°
2️⃣ 80°
3️⃣ 100°
4️⃣ 135°​

Answer 1

Answer:

The largest angle has a measure of 75°.

Option 1 is the correct answer.

Step-by-step explanation:

Given that, One of the angles is 75°.

Let's assume that, the greater of the remaining angles has a measure of x°.

According to the problem, remaining angle is (x - 35)°

We know that, all angles of a triangle sum up to 180°

∴ 75 + x + x - 35 = 180

∴ 2x = 180 - 40 = 140

∴ x =$\frac{140}{2}$ = 70, The given angle is greater than this one.

Therefore, the largest angle has a measure of 75°.

Answer 2

Answer:

Question

One of the angles of a triangle is 75°. If the difference of the remaining two angles is 35°, then the largest angle of the triangle has a measure of ____.*

Concept used

Here the concept of angle sum property is used.

✏️The sum of interior angles in a triangle is 180°.

Solution

Let us assume the measure of unknown angles be x° and y°.

Given

☞If the difference of the remaining two angles is 35°.

➝This statement means x°-y° = 35°

➝x=35° +y°

Now,

$\sf{75 \degree + x + y = 180 \degree}[angle \: sum \: property] \\ \sf{75 \degree + 35 \degree + y + y= 180} \\ \sf{2y \degree = 180 - 110} \\ \sf{y \degree= \frac{70}{2} } \\ \sf{y \degree = 35 \degree}$

we know

➝x= 35° +y

➝x= 35° + 35°

➝x= 70°

Now ...we see that 75° is the largest angle in the triangle.

therefore option 1 ) 75° is correct .