The problem asks to find the size of angle $DAB$ in the quadrilateral $ABCD$. We are given the angles at vertices $D$, $C$, and $B$. Angle $ADC$ is $96^\circ$, angle $BCD$ is $90^\circ$ (indicated by the square symbol), and angle $ABC$ is $67^\circ$.

GeometryQuadrilateralsAnglesAngle Sum Property
2025/6/22

1. Problem Description

The problem asks to find the size of angle DABDAB in the quadrilateral ABCDABCD. We are given the angles at vertices DD, CC, and BB. Angle ADCADC is 9696^\circ, angle BCDBCD is 9090^\circ (indicated by the square symbol), and angle ABCABC is 6767^\circ.

2. Solution Steps

To find the size of angle DABDAB, we use the fact that the sum of the interior angles of a quadrilateral is 360360^\circ. Let xx be the measure of angle DABDAB. Then,
x+96+90+67=360x + 96^\circ + 90^\circ + 67^\circ = 360^\circ.
Combining the known angles, we have:
96+90+67=25396^\circ + 90^\circ + 67^\circ = 253^\circ.
So,
x+253=360x + 253^\circ = 360^\circ.
Subtracting 253253^\circ from both sides, we get:
x=360253x = 360^\circ - 253^\circ.
x=107x = 107^\circ.

3. Final Answer

The size of angle DABDAB is 107107^\circ.

Related problems in "Geometry"

The problem asks to identify the hypotenuse, the opposite side to angle $\theta$, and the adjacent s...

Right TrianglesTrigonometryHypotenuseOpposite SideAdjacent Side
2025/7/21

The problem asks to identify the hypotenuse, the opposite side, and the adjacent side to the angle $...

TrigonometryRight TrianglesHypotenuseOpposite SideAdjacent SideAngle
2025/7/21

The problem asks us to find the value of $y$ in two right triangles. In the first triangle (a), the ...

Pythagorean TheoremRight TrianglesTriangle PropertiesSquare Roots
2025/7/21

The problem asks us to find the value of $y$ in two right triangles. In the first triangle, the angl...

Pythagorean TheoremRight TrianglesTrigonometry
2025/7/21

We are asked to find the value of $y$ in two right triangles. a) The right triangle has a leg of len...

Right TrianglesPythagorean TheoremTrigonometry45-45-90 Triangle30-60-90 TriangleSineCosine
2025/7/21

The problem asks us to find the value of $y$ in two right triangles. a) We have a right triangle wit...

Right TrianglesPythagorean TheoremTrigonometry45-45-90 Triangles30-60-90 TrianglesHypotenuse
2025/7/21

The problem is to find the length of $HJ$ and the measure of angle $GJN$ given certain information a...

TrianglesMediansAngle BisectorsAngle MeasurementSegment Length
2025/7/21

We are given that $\overline{EJ} \parallel \overline{FK}$, $\overline{JG} \parallel \overline{KH}$, ...

GeometryTriangle CongruenceParallel LinesASA Congruence PostulateProofs
2025/7/16

We are asked to find the value of $y$ in the figure. The polygon has angles $4y$, $4y$, $5y$, $2y$, ...

PolygonInterior AnglesAngle Sum Formula
2025/7/16

The image shows a circle divided into sectors. We are given the degree measures of three sectors: $7...

CircleAnglesSectorCentral Angle
2025/7/16