Question

Need help solving with working much appreciated

Answer 1

i. g = 70°

ii. x = 85°

Explanation:

Given:

Let first we name the triangle

i. ) Δ PQR , m∠ PRQ = 40°

ii. ) Δ ABC is a right angle at B and a line B- D-C

m∠ DAC = 25°

m∠ ACD = 60°

m∠ BDA = x°

To Find:

i. g = ?

ii. x = ?

Solution:

i.

In Δ PQR , PR ≅ QR ...........{Given]

∴ Δ PQR is an Isosceles Triangle.

c.........{ Base angles of Isosceles triangle are equal }

∴ m∠ PQR = m∠ RPQ = g

Now sum of all the angles in a triangle is 180°

∴ m∠ PQR + m∠ RPQ + m∠ PRQ = 180°....{Angle sum property of Triangle}

`g + g + 40 = 180\\2g=180-40\\2g=140\\g=(140)/(2) \\g=70\°`

∴ g = 70°

ii.

We know sum of all the angles in a triangle is 180°

In Δ DAC

m∠ DAC + m∠ ACD + m∠ ADC = 180°.....{Angle sum property of Triangle}

`25+60+ \angle ADC = 180\\`

`\angle ADC = 180-85\\\angle ADC =95\\`

Now By Linear Pair Angle Property

m∠ ADB + m∠ ADC = 180° ........{Linear Pair Angle Property}

`x+95=180\\x=180-95\\x=85`

∴ x = 85°